There is a lot to say about both RV and motel/car ways to travel. Usually, RV is a choice of a lifestyle rather than a way to save money. By the time you rent the rig, pay for the other fees involved and then the actual fuel that you will use (more than a car), the motel is usually cheaper. Here is a thread debating the two travel means. I am curious, though, about two things. It is difficult to find a place that rents a travel trailer, so where are you planning to rent from? Also, do you already own a suitable tow vehicle?

Now, on to your other questions:

1. Recommendations on time spent in each park?
Grand Tetons - a day is fine unless you plan to do some hiking, boating, or other sports. Add time accordingly.

Glacier - at least a day, adding time once again for any sporting activity you might want to do.

No Yellowstone?????

Banff - at least a couple of days, particularly if you want to drive up Icefields Parkway towards Jasper (highly recommended).

I can't answer about Nez Perce -- never been there.

2. Places to stay?
It will depend on what you finally decide to do about your overnights. Grand Tetons, Glacier, and Banff all have campgrounds without hookups. Lake Louise (north of Banff) has an RV section with electric hookups, but no water or sewer. (They have a place to load your tanks with water, and a dump station.) All three have hotel facilities within the parks and just outside of the park. (Warning: Jackson, WY is EXPENSIVE. The Motel 6 in Jackson is $189/night in the summer! Commercial RV parks are also high, for RV parks.)

3. Top things to do within each park?
Each of the parks has a website that will detail what there is to do once there. All of them, of course, include sightseeing drives, photography, and hiking.

Grand Tetons

Glacier

Banff, Canada (I'm assuming you have your passports in order, and if renting a vehicle, permission to cross the border with it -- in writing.)

Nez Perce


Donna