Loire, Bordeaux and ? N

You can fly non-stop from Bordeaux to Barcelona on Vueling ($68) and Iberia ($105). Vueling is a low-cost carrier so if you check a bag, it may cost as much as flying on Iberia. You can also fly non-stop from Bordeaux to Amsterdam for $157 on Air France.
If you go to ES, you can take direct trains from: Barcelona to Granada (6h 30m), Granada to Sevilla (2h 45m) and Sevilla to Madrid (2h 45m). I would also take a day trip to Toledo from Madrid (45m).
If you fly to Amsterdam from Bordeaux, consider flying home from Brussels.

When in the spring? That could affect whether people recommend that you head north from France of south. Andalucia can be lovely even in April; I don't like chilly, wet weather and would never choose to visit the Netherlands or Belgium at that time of year. (You might make a different decision if you're interested in the flower market in the Netherlands.) Even down around Bordeaux I think you'll find it not warm and sunny for much of the spring. (Yes, I'm hyper-focused on weather when I plan a trip.)

I liked Bordeaux, but I'd say it's less engaging than Lyon (much less Paris), so to me a trip to that area really calls for time in the Dordogne and/or Lot. I managed to see a lot by public transportation, but not everything I would have liked to see. The Dordogne is easiest if you're willing to rent a car for a few days. In addition to beautiful villages and great scenery there are castles and rivers to float down (probably kayaks are available). Among the towns I visited (I took a lot of side trips) and especially enjoyed were Cahors, Perigueux, Figeac and Sarlat-la-Caneda (with a large market on Wednesday and a huge market on Saturday). It's a measure of how much I like medieval towns, I guess, that I sing the praises of Sarlat despite having been rained on--hard--during most of my day-trip there.

Much of Bordeaux feels the opposite of small, but I think you'll find the medieval area appealing.

Closer to Bordeaux than the Dordogne is the small town of St-Emilion, which has elicited varied responses on this forum. It's a medieval town with lots of restaurants. It's extremely popular with wine lovers (of which I am not one). It was awash in tourists down near the foot of the hill, but I found it much less touristy in the upper part of the town and thoroughly enjoyed walking around for several hours. Some others really, really disliked the touristy aspect of the place. In any case, it's doable as a day-trip from Bordeaux, but the train station is quite a hike from the town. There's a little tourist vehicle (runs on the road but looks like a train) that will take you from the RR station to the top of the town for a very modest cost--I think around 4 euros one-way. I recommend doing that so you can take the easy stroll downhill. Note, though, that this is a bit of a tricky destination when it's wet; some of the streets are quite steep and cobbled, and they get slippery in the rain.

Since you like smaller places and I think you'll use up a lot of your time in France (a week in the Dordogne would be lovely), I'd recommend you consider the Basque Country in northern Spain if your trip will be late in the spring. That's another cool, damp area, so it wouldn't be my choice earlier in the year. But it's very near the French border. For an early- or mid-spring trip, I think MaryPat's onto something with the Barcelona suggestion. I love the city--can't get enough of the modernista architecture--and the climate is very moderate. However, it is a big, touristy place, so I suspect it wouldn't be a place you'd want to spend a lot of time (though I was happy to spend 10 days there). Just up the rail line is the lovely, historic smaller city of Girona. That might be more your style.

I won't recommend any hotels or restaurants because my taste in hotels runs to "as cheap as possible" rather than "most charming" and I tend to organize my days around public-transportation schedules rather than meals (more's the pity).

Several years ago we visited the Loire area and based in Amboise for a couple of nights. It was enjoyable with it's own attractions and the Chateau de Chenonceau was nearby.

The Loire Valley is spread out, so it's not well suited to bicycle touring unless you are really athletic. It's much more convenient to have your own car. We stayed in Azay-le-Rideau at the Hotel Biencourt, which we absolutely loved. We'd stay there again in a heartbeat. The building is very charming, literally a stone's throw from the chateau, serves a great buffet breakfast, and our room was very comfortable and quiet. The innkeepers were incredibly helpful.

The town is really a small village, but with a surprising selection of good restaurants, simple and high end. It is far enough from Paris that it doesn't attract many day tours, so it's much less crowded than the ever-popular Amboise. From Azay it was about a 45-min drive to the Fortress of Chinon. We wish we'd had a whole day in Chinon to do the walking tour of the old town; the fortress itself has a lot to see with interpretive signs and motion-activated video and sound effects, also an excellent gift/book shop. Another day we drove to Chenonceaux, about 60-75 minutes each way. We would have branched out from Azay to see more of the chateaux at the western end of the Loire region, but had to cut our visit a bit short because of a ferry cancellation.

Navigation tip: If you're driving from Paris or other points north heading south on the A10, when you go through Tours there's an autoroute exit for Azay. If you take it you'll be on decidedly un-scenic surface streets for quite a few miles before you connect up with the D751. (We did this -- not fun at the end of what was already a long day.) Ignore that exit and continue through Tours to the A85 (direction Angers, I think -- in any case, westward) and then exit on the D751.