Keep your camera in your camera bag at all times, except to take pictures. Do not change lenses on the beach. Be sure that you have a filter on the lens. Stay away from kids who kick up sand. Pay attention to wind strength and wind direction. Bring a fine brush to clean your camera if needed. I dropped my D7100 in the sand in Nicaragua a few months ago. It just slipped off a low table so it was not damaged. (If you have to drop your camera, sand is not a bad place to do it.) I brushed off the sand for half an hour with my toothbrush. So you see that I speak from experience. My camera is fine, by the way. Enjoy your trip to the beach, and take lots of pictures!

I travel to Germany at least once a year for work, usually for 4-6 weeks. For several years, I traveled with a D7100--I have the same three lenses you do. (I just bought a SONY A7 III.) I found the D7100 and the 18-140mm to be a very competent combination. I hardly ever used the 55-300mm because the 18-140mm has a good range and because I think that it is the better lens. In fact, the 55-300mm often didn't even make it into my travel bag. As I do a fair amount of architectural photography (as well as landscape), I decided to add the Sigma 10-20mm, and I generally got good results from it. So I would take the 18-140mm and the Sigma 10-20mm.

I agree with others that you should experiment with your settings. I would set the aperture at 5.6 (one or two steps above the maximum aperture at the respective focal length, but not higher than 8) and shoot at 1/125 or faster. This should enable you to set the ISO at 100 or 200 during good daylight--which should help you avoid a noise problem. Many lenses do not perform as well with a small aperture as you only use a small percentage of the glass. Once you get a handle on the focusing issue you can experiment with smaller apertures to achieve a larger depth of field. If that does not help try shooting with a tripod. Enjoy your trip!

I spent two weeks in Sicily in 2015. We rented two apartments for a week each, the first in Acireale (just north of Catania) and the second in the old town of Cefalù. We had a rental car for the entire two weeks. One thing to keep in mind is that Sicily is a big island. You will have a limited reach for day trips from Taormina. As long as you travel on the Autostrada you will move quickly. Traffic on all other roads, on the other hand, moves slowly as most of Sicily is hilly and roads are winding. We drove from just south of Taormina to the North Coast via Randazzo. It was a beautiful drive, but it took over three hours. So reaching the stunning Norman cathedrals (with Byzantine mosaics) in Cefalù, Palermo and Monreale in day trips will be next to impossible. Recommended day trips: Mount Aetna, Catania (Baroque center and Roman theater), Siracusa (Greek theater and old town with the stunning Piazza del Duomo), and the gorgeous Baroque cities further south like Noto, although reaching some of the other Baroque towns of the Val di Noto may be too time-consuming. And of course Taormina itself. As someone pointed out, all the Greek temples tend to be in the South and West and therefore out of reach. Even in two weeks, we only got to see a fraction of what we really wanted to see. Sicily is a stunning place in every regard, and the food is amazing. Enjoy your trip. Here is a selection of pictures I took on that trip.
https://www.flickr.com/photos/zug55/albums/72157654759174060

The V&A Waterfront is the iconic spot where many of the classic Capetown pictures are taken. There are other great parts of the city, such as Camps Bay. Going up to the Table Mountain is a must--you get grand views over the city, Robben Island (if its is not hazy), and the mountains around it. If you have the opportunity, I would take some trips into the surrounding areas. Take a tour of Robben Island. We rented a car which makes getting around a lot easier. Worthwhile day trips are driving to the Cape and to the wine country around Franschhoek--you also could stay overnight. If you have more time, drive along the Garden Route along the Indian Ocean coast to Hermanus (whale watching) and beyond. This is a gorgeous coastal landscape like the Big Sur, just more beautiful. There will be ample opportunity of both urban and landscape photography. So your 24-105mm is a good start. The rest depends on your photographic style and on the amount of equipment you want to carry. You will have ample opportunity to use a wider lens. I personally like landscape shots with a telephoto lens. Tripod? The question is always how mobile you want to be and how much you want to carry around.

What lens to use for landscape photography depends on your personal style, on your sense of aesthetics. Landscape shots taken with an ultra-wide lens can be very dramatic if you are able to integrate some interesting foreground features that pull you into the image. This is a skill I still struggle with--but admire when I see it in pictures taken by others. I have a Sigma 10-20 for my D7100 but seldom used it for landscapes. Most of my landscape images are in the mid-range. I also take many landscape images in the telephoto range. This allows me to work out an interesting feature in a landscape without the clutter an ultra-wide image often delivers. So my advice would be twofold: look through your landscape images you like and check at what focal length you shot them. Then go out with your lenses and experiment. Take shots at the entire range of focal lengths and decide what works for you.

Somehow many here miss the real point. We are not talking about sex, after all. If you like a heavy camera, great. If you like a lightweight one, great as well.

I travel internationally a lot. I usually carry my camera bag all day long and do a lot of street and architecture photography. (I also carry a Canon G9X for moments when I do not want to show my big camera.) So weight really matters to me. I have been shooting with a Nikon D7100 for a while. I have been looking for a full frame camera to get close to professional image quality for blogging. When the new D850 came out I was ready to get it--until I held it in my hands and realized how heavy that monster is. So I decided to go with the new SONY A7 III instead--it just arrived yesterday. I got the 24-105 f/4 with it, and I am choosing some prime lenses by quality and weight.

The point is, having a lightweight and smallish camera is really important to me because of the travel photography I do. That does not mean it has to be important to everybody else. So why be judgmental about it?

Northern highlands of Nicaragua

The previous two posts made me check into the Tamron 18-400. It indeed is a DX (i.e. crop sensor) lens. But check out the description of the lens on the Tamron web site:
http://www.tamron-usa.com/product/lenses/b028.html

"Introducing the world’s first ultra-telephoto all-in-one zoom lens for the APS-C format. With a focal length range of 18-400mm and 22.2x zoom, it has an ultra-telephoto range equivalent to 620mm in the 35mm format."

How can this be? If it is an APS-C / DX format lens, how can you use it on a full frame (FX) camera body? Brucej67 correctly points to the problems with that. What I do not get is how you get a crop factor (620mm!!!) when you put a DX lens on an FX body. In my humble opinion, the Tamron web site is misleading, and the B&H web site just copied this BS onto their web site.

FX lenses are constructed to expose the entire sensor on a FX camera. DX cameras have a smaller sensor. So if you put an FX lens on a DX body, the lens sends more information (a larger image) to the sensor than the smaller sensor can accept and record. The smaller sensor only records the center of the image, but not the outer fringes. So the edge of the picture gets cropped away by the smaller sensor, hence the crop factor. The factor between FX and DX is about 1.5. So at 400mm, you get an image as if you had a 600mm lens. Remember, this only happens if you put an FX lens on a DX body. The beauty of this is that your DX sensor still records a 24 MP image--but you de facto have greater magnification. So this is not the same as cropping your image on your computer--there you actually lose megapixels, and the quality of your image decreases. I hope this helps.

I was in León, Nicaragua, in December. The Momotombo Volcano was quiet then.
https://www.flickr.com/photos/zug55/25881119017/in/album-72157694175340765/
However, the Telica Volcano nearby was smoking. There are several active volcanos in Nicaragua.