When you enter a public restroom with a long row of stalls always walk way down towards the end then count back 1 or 2 and THAT will be the cleanest stall.  Most people either take one of the first 2-3 or the very last one, thus those get the most use and are the dirtiest.  Best of all, if you find a restroom that loops around to another set of stalls - go off into remote territory!  Those stalls will be cleaner than any nearest the door. 

Now, if you thought this was a more general guide, here are some other pointers from someone who has pee'd all across the country:

- all hotel/motel lobbies have public restrooms and they are cleaner than fast food restaurant ones (such as when you pull off the highway); find the ritziest hotel off the exit and waltz into the lobby.

- libraries and town offices are also a good place to stop

- no liners in the stall?  use toilet paper - make a large triangle with the paper across the seat

- flush with your foot/bottom of your shoe so you don't touch the handle

- hold your paper towel in your hand as you open the door to leave so you don't touch the door

- pregnancy and/or a 2 year old holding himself will suddenly make many restrooms available to you despite their "employees only" signs

Don't cut back on the beverages and enjoy your next car trip!