Hi Eric,
I live at the Frankenjura in Germany. Since it hasn't been mentioned yet, I feel like I'd be letting down my chosen home by not representing! There are 10,000 sport routes here from 5.1 through 5.15b, with short approaches and often time great moderates directly next to hard routes. If not, then there's always another near-by crag with something for one of you. Your mentioned season is perfect for visiting here, but I almost wouldn't recommend visiting if you weren't going to come in late Spring/early Fall. It's doubtful that you'll need a sweater to stay warm while spending time in town, but if you've got a light jacket that you're bringing anyway in case it rains, then you'll definitely be fine. This week I'm wearing no more than a sweater while walking around. The food is great (and dirt cheap!), but might get a little one-sided if the local fare is all you eat while you're here. Accommodation is cheap and you can find lots of different locations in the area without having to travel far. If you base in Nürnberg or East of there (like Hersbruck), you can work on routes in both the northern and southern Frankenjura. There are also several cities worth visiting in the area without having to leave it, as I understand is one of your criterias. You definitely need a car though, unless you're really hard-core and willing to bike everywhere with a full pack of climbing gear. There are a few crags within walking distance of train stations, but for the majority of the crags you'll want a car. For day trips away, there's Prague, Innsbruck, Munich, Salzburg, Rothemburg o.d. Tauber, Würzburg, and the best of them all: Dresden, all within a couple of hours' drive. If you want to try different flavors of climbing, you'd have to move base camp, but you can get granite and sandstone in addition to the limestone here. It's all on the Germany page here on MP.
If you'd prefer Italy, Finale Ligure is certainly a great destination, but I felt like you need more rest days there as the rock was extraordinarily rough for limestone. After max. 2 days we definitely needed a break so our skin could replenish. Southern France isn't too far away if you'd like to see Ceuse and Buoux. This trip is almost certainly pricier than the Germany suggestion above.
Turkey is certainly cheap, but also very dirty and, in my opinion, annoying. It's also not as safe as Germany, but possibly on par with Italy and France. It's hard for me to gauge "safety" because I never felt unsafe in any of these areas. I've never climbed in Turkey, but my wife has and she said the climbing was fun.
My last suggestion is Croatia. There is lots of climbing there and easy access to the Adriatic Sea. We didn't do a lot of climbing or go past the northern peninsula, but a bit further south is an awesome gorge in a national park with great climbing.