Near Heidelberg

Chris- I assume you will be driving up A5 to get to Frankfurt. There is a nice town called Gengenbach (sometimes called the Rothenburg for Germans)that is a few Km east of A5 just south of Offenburg. This is about a 2.5 to 3 hour drive to the airport. There are several hotels in your price range and several slightly higher. We actually stayed in a very nice hotel about 2 KM west of Gengenbach in Berghaupton , the Hotel Restaurant Hirsch. Their comfort double was really nice, albeit around 90 Euros including excellent breakfast and free parking. Excellent restaurant on site or you can do the short drive into Gengenbach for supper. You would get there early enough to visit Gengenbach in daylight.
Have a safe trip!!!

M favorite recommendation is Bad Urach.

If you are flying out in the afternoon, Hirschhorn has a castle that has been turned into a hotel. It is very nice and not too far from Heidelberg.

I've spent almost 2½ weeks, total, in 4 trip staying in a beautiful little Black Forest Spa town called Bad Herrenalb. It's about 40 min by streetcar from the train station in Karlsruhe. My advice, ditch the car in Karlsruhe the day before and take the streetcar to Bad Herrenalb. It's a very picturesque little town in a valley in the Forest - good hiking and a traditional spa. Here is a good place to stay; reasonable price and a short walk to the streetcar station. If you leave at 9 AM, you can take the streetcar into Karlsruhe Hbf (free with Konus Card), then catch an ICE (1 hour) and be at the Fernbahnhof at FRA just after 11, with no car to check in. There are similar trips every hour (Lv 10 AM, Ar noon, etc). If you are flying Luftahansa, you can check any luggage at the Fernbahnhof and walk across the pedestrian bridge to Terminal 1.

Thank you for all the feedback. We really want to be staying within an hour or less from the airport, though. We will be traveling with two children under the age of 3 and in the interest of both us and our fellow passengers having a peaceful flight (ie. them sleeping as much as possible), we would like to minimize the drive to the airport. It doesn't have to be Heidelberg, of course, it is just a logical stop on the way north from the Berner Oberland, which is about an hour from the airport. We are definitely open to other suggestions.

Oberwesel is an old-world wine village between Bacharach and St. Goar on the Rhine river with old town walls (and walking paths atop the walls) and towers just one hour by direct train from FRA (fare is 14.80€.) You can drive from O'wesel to FRA, but I would do as Lee suggests and ditch the car (probably in Mainz or Koblenz) prior to Oberwesel so as to avoid traffic snarls. The train takes you directly into the airport terminal. There are 6 direct trains between 5:30 and 12:00 on weekdays. Weinhaus Weiler gets great marks but might be over budget. Cafe Bonsch is a bakery that offers nice-looking double rooms w/ bath in the heart of town. Prices are in your budget and include breakfast. Cafe Bonsch Liebfrauenstr. 45 55430 Oberwesel Telefon: (06744) 2 64
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Since you want to be in between Heidelberg and the airport, but also close enough to Heidelberg to visit, the easiest thing to do is to pull up a Google map and pick out a town that fits that part of your wish. Then go to the towns website to see if it also matches what you are looking for. Tom knows this area the best, so hopefully he will come make some suggestions for you. He travels around and visits these small towns a lot. Ladenburg or Weinheim might fit the bill for what you are looking for:
http://www.weinheim-marketing.de/index.php?option=com_content&task=view&id=1&Itemid=4

Jo beat me to the Weinheim recommendation. Has two castles overlooking the town, a lovely Altstadt and Schloss garden. The only stipulation would be to stay within the Altstadt, because the rest of the town is fairly modern and/or industrial. Ladenburg is also a good choice for a one night stay. It still has most of it's medieval wall, and there's a very attractive park along a scenic bend of the Neckar river. Nearly everyone I've showed Heppenheim to has the same reaction- "Why isn't this town in any guidebooks?" The only caveat I'll give is that I only know of one hotel in the Altstadt, and it seems to close for no apparent reason for weeks at a time. All of the above are located just off of A5 within 45 minutes of the airport. Someone also mentioned Hirschhorn, which is another good recommendation, but I'll just point out it's probably a good 90 minute drive to the airport. I think Darmstadt is an under-rated city, but from what you wrote, this doesn't seem like what you're looking for.