Both. An inflatable with a small motor for covering distance and kayaks to paddle further as needed. Most likely sleeping on the boat.
Well, there are six backcountry campsites on Yellowstone Lake that handle motorized craft. It's my understanding that three have docks and three where you have to anchor your boat off-shore. Of these sites, all are located on the western side of the lake with two of them located on Frank Island. The rest of the campsites along the lake are for canoes and kayaks, and some of these water craft ones are available to folks who backpack in also. If you stay at one of the sites for paddlers, then you must completely remove your boat form the water while at camp. I've canoed the lake several times but have never used a motorized boat so you will want to check with the main backcountry office at Mammoth for motorized regulations.
There are three arms to the lake (Flat Mountain, South and Southeast) that have speed and or craft restrictions - The South and Southeast Arms have a 5 mph zone that eventually as you head south, becomes a paddle only zone. Flat Mountain Arm does not have the speed restriction but does have a paddle only zone as you head west.
Red Campsites - Motorized and/or Paddle ------
Blue Campsites - Paddle only ------
Orange Campsites - Paddle or Backpacking
Wildlife opportunities and things to do - First off, if you are not making any noise (floating by) you might be able to see wildlife along the shore of the lake itself. I have seen moose, deer, otters, muskrat, bald eagles, golden eagles, osprey, pelicans, ducks and other waterfowl simply by floating by them. Obviously there are opportunities to see wildlife if you plan on doing any day hikes while on your trip particularly if you hike into the Thorofare area.
As far as things to do are concerned, If staying at campsite 7L5, you could off-trail up the drainage to Delusion Lake. This lake is seldom seen and might be worth your time. Disclaimer: you've got about three quarters of a mile of old burn that you will have to negotiate to get to the wetlands on the east side of the lake. If staying at 7M1, you might explore the drainage that leaves Flat Mountain Arm to the west. When I did this a number of years ago, I saw numerous grizzly tracks, a complete moose skeleton, and two large bull elk as I hiked along the stream. You should take a couple of days and explore the Southeast Arm. On one of the days, hike (off-trail) to the top of Laingford Cairn which is located slightly northeast of campsite 5E2. From the top, you get a commanding view of the Yellowstone River Delta plus a look into the Thorofare to the south. On day two, take a long day hike into the Thorofare itself. You will be making your way through extremely wild country with the potential of more wildlife encounters - wolf and bear track might just be more common than boot prints along your way. Another opportunity for you would be to off-trail into Brimstone Basin which is located off-trail about three quarters of a mile to the northeast of campsite 5E4. It is a large thermal area that tends to look like a moonscape with a few steam vents spread throughout. While it doesn't have geysers or mud pots, it still has some other world charm to it and from the area you can get a nice perspective of Yellowstone Lake and the Promontory to the west.
Well, I hope this gives you a few ideas. There are plenty of areas to explore around the lake if you are willing to take the time and do a little off-trail wandering.
