We are visiting Yellowstone National Park in the last wee of May, which places are “must see”?

What kind of clothing should we carry? Are the tourists allowed to bathe and play at the Tower falls?
Which hotel or cabin is the best place to stay around Mammoth Hot Springs area? I mean, with respect to the view, tidiness, etc.

At this late date I doubt that you will find any lodging accommodations in Yellowstone National Park other than cancellations. Reservations for popular parks like Yellowstone should be made well in advance (9-12 months). However, if you hurry you may find accommodations available in the towns just outside the park like Gardiner located north of Mammoth and West Yellowstone located just outside of the west entrance to the park. There are other towns like Silver Gate to the northeast, Cody to the east and Jackson to the south. However, I suggest Gardiner and West Yellowstone because they are closest to the primary areas of interest in the park. I’ve stayed in both Gardiner and West Yellowstone and recommend you stay in West Yellowstone. There are many motels to choose from and I suggest you look them up in “www.tripadvisor.com”. I can recommend Yellowstone Park Hotel on Grizzly Ave in West Yellowstone. It’s clean, comfortable and they serve a complimentary continental breakfast. Be sure to spend a couple of hours visiting the Grizzly and Wolf Discovery Center near the hotel to see mature grizzlies and a pack of wolves. It’s interesting and you may never get to see these animals in the wild.

I don’t recommend you swim below Tower Fall and the reason will be obvious when you see it. I was going to suggest that you go to the 45th Parallel Bridge and Boiling River located between Mammoth Hot Springs and Gardiner on the east side on US-89 but that will probably be closed due to high water caused by spring runoff. But if you’re ever in Yellowstone during the mid to late summer months, check it out.

Yellowstone National Park is large and seeing it involves much driving. You’ll have to return to your “home base” each night but I think that’s better than packing up and moving every couple of days. You should split the park into sections and visit one section per day. Following is a suggested itinerary. You can use it as a guide in deciding how you want to see the park in the number of days you have available.
First of all I suggest you download the “park map with detail” from the following web page in PDF format and study it to familiarize yourself with the park.
http://home.nps.gov/applications/hafe/hfc/carto-detail.cfm?Alpha=YELL#
Also, download the map of Grand Teton NP.
http://home.nps.gov/applications/hafe/hfc/carto-detail.cfm?Alpha=GRTE#

Day 1: The Geysers & Hot Springs
Firehole Canyon Drive
Lower Geyser Basin
Firehole Lake Drive
Midway Geyser Basin
Upper Geyser Basin (Old Faithful)

Day 2: Grand Teton NP
Biscuit Basin (Yellowstone)
Blacksand Basin (Yellowtone)
In Grand Teton National Park:
Coulter Bay Visitor Center
Jackson Lake Lodge
Signal Mountain
Jenny Lake

Day 3: Yellowstone Lake / Hayden Valley / Canyon
West Thumb Geyser Basin
Bridge Bay – boat tour
Lake Village
Mud Volcano
Sulphur Caldron
Hayden Valley (look for wildlife)
Canyon Village Visitor Center
Upper and Lower Yellowstone Falls (time permitting)

Day 4: North Loop
Norris Geyser Basin
Virginia Cascade
Upper and Lower Yellowstone Falls (if you missed all or part of it from the previous day)
Mt Washburn (if Dunraven Pass has been plowed open)
Tower Fall
Petrified Tree
Mammoth Hot Springs Terraces
Obsidian Cliff

If Dunraven Pass is still closed you will have to get to Tower via Mammoth Hot Springs. Or, you can skip it because it’s a long way to go for one of the lesser attractions in Yellowstone. You can also skip the Petrified Tree because it pales in comparison to Petrified Forest National Park.

Day 5: Gallatin River
Paddle & Saddle – http://www.montanawhitewater.com/index.html

The horseback ride is more of a novelty for those that don’t get to go horseback riding very often, like me. On the other hand, the whitewater rafting on the Gallatin River is fantastic. This is not a “float” down a lazy river. This is whitewater, especially in May during the spring melt. The Paddle & Saddle includes a half day horseback ride followed by the Classic Half Day on the Gallatin. Or, you can skip the horseback ride and take the Classic Full Day on the Gallatin. You’ll have to wear wet suits, neoprene booties and helmets because of the cold water and rocks. Great fun – highly recommended.

As far as dress is concerned, late May can be warm when sunny and bone chilling when overcast and windy. Bring your shorts and T-shirts but also bring warm clothing and dress appropriately for the weather. Carry a jacket and perhaps a rain coat or poncho in your backpack just in case you get caught far from shelter. You can get more information from the NPS web site.
http://www.nps.gov/yell/

One last note, take heed of wildlife warnings. The animals may seem to be docile but they are wild and can charge you at any time. This is especially true if you invade their space by getting too close or surrounding them. Be safe and have a lot of fun. I know you’re going to enjoy this trip.