Most of the dental schools in the country are in fairly large cities, which is good for budget travelers because it means you can use public transport! This can save you a TON of money.
When you get an interview invite, the first thing to do is to look into what sort of public transportation is available. Some schools might provide you with a list of options, in my case I had to do most of the searching on my own. If you can, book a hotel that is close to a bus or subway route that covers the airport and the school. If you have to (this is most often the case) you can find transfer locations between bus/subway lines to get you where you need to go. Print schedules and maps ahead of time, and familiarize yourself with them. You might also want to bring a compass along with you if you are bad at orienting yourself, because you might walk in the wrong direction by accident (like I did in Cleveland at 6 am). Once you have a good route planned out, go ahead and book your flights and hotel, but keep in mind that buses and subways might not run at all times, so take this into consideration.
As far as traveling itself. I wore my whole suit on every flight to prevent excess wrinkling. Uncomfortable? You bet. I didn't have wrinkles though! Additionally, I didn't use a suitcase. Instead, I used my backpack (which is large, but not anything that looks odd when I wear to school every day!) and only packed the few things I would need for an overnight trip. If you plan properly and pack well, you can easily live out of a backpack for two days. The advantage to using a backpack is that you can take it with you on all the interviews without looking silly and toting a suitcase. These places are schools. Backpacks don't get a second look, and they do the job of a suitcase just as well!
So now you have all your luggage and traveling needs covered. Seriously, use public transport. It can get you where you need to go for cheap! When I interviewed at Nova, getting from the airport, to the school, and back was FREE! A cab would have probably cost about 30 bucks each way. My expenses for an interview (Including airfare, hotel, and transport) never went over $350, and I never flew less than 1500 miles.
Plan well, and you can save money and hassle!
Also, you get to have some fun stories, like being lost in Cleveland at 6 am until a nice bus driver tells you where the hell you need to go!