Just about any place can handle the 35mm negatives, including Walgreens, but for other types you will probably have to go to a full-service photo lab, and maybe even a professional lab. Never hurts to ask, though; Walgreens might have the machinery to print your other types of negatives.
I haven't developed or printed film pics at Walgreens in several years (since I went digital), but I used to get mine developed at the Walgreens stores around WDW all the time. All of the Walgreens photo labs I dealt with dow there had terrific service, nice people, and did an excellent job of developing and printing my pics. If you go to Walgreens for your reprints, I think you'll wind up pleased with the results; just explain in a friendly fashion that the negatives are quite old and pretty irreplaceable, and the lab tech will take good care of them.
For clarification:
a) One-hour labs like Walgreens do not send pics out - they have the machines right there, that's why they can get pics developed in 1 hour. However, most 1-hour labs have machines that can only handle 35mm or APS film and negatives.
b) Negatives are already "developed." What you want is called "reprints." This is usually a bit cheaper than "processing", which includes both developing and printing.
One other recommendation: As soon as you get the prints home, you should scan them at hi-res so that you will have digital copies that you can back up in case the prints and negatives are ever lost. You can also use software like Photoshop Elements and Noise Ninja to clean up the scans and make the digital pics look at least as good as the prints, maybe better.