Go online and get the visitor information and maps for the area, the park and other surrounding areas - south of the park is the Grand Tetons - some of the most beautiful country around.

Just outside of West Yellowstone, is the Madison river and Hebgen (earthquake) lake - very interesting and pretty.

4 days is a short trip for the park -
You will be entering on the west side - study the map and routes - be prepared for road closures - construction and areas being closed off -

Check with the park for planned closures -

Make backup plans -

I would recommend the standards - geyser, morning glory pool, grand canyon of Yellowstone, upper and lower falls, mud bogs -

Lots of walking trails - but they eat up time - try to stick to the major sits.

Not sure when you will be there, but plan on long days and slow traffic -
people just stopping their cars in the road to get pictures - lots of traffic jams...

Drink lots of water to prevent dehydration and altitude sickness...

Have fun :)

Since my visit there I found a few sites (not bookmarked, unfortunately)that give you a list of spots just off the frequently trodden path that'll give your pics a different aspect whether from a DSLR or P&P. I expect someone on here will know of one.

Map out a route and use these to extend a visit to any one place, get a more memorable shot that not everyone else has, and just ease off on the constant convoying of people around.

Or hire a coach and driver that can take the whole party on one bus.

Like to be of more help, but I've only been there once myself and as much as I'd love to revisit there's more more world to get to first.