I was there off and on for over 3 months last year. Stayed in JoSiTo camping the whole time.The campsite is a very social place - which was a big plus for me as I was travelling solo. In fact, I made enough contacts in the first 2 months there to keep me busy with friends and climbing partners for the rest of the year travelling throughout Europe. From my experience, climber's garden is a much quieter campground where you can enjoy your own space a little more. Not much difference in price or in facilities between there and JoSiTo.
Best season is from October - April. Before/after that it gets very hot and you can only comfortably climb in the shady sectors. You can rent a gas cooker for 1 euro/day (but almost always people don't mind you borrowing their's). On Sunday the small town (Akdamlar) at the base of the mountain has a bazaar where you can buy super cheap fruit and vegetables for the week's cooking. On the way to Antalya there are many large supermarkets (Migros, Kipa Extra, etc.) where you can buy almost anything you need. I never had any problems hitchhiking - I did many trips all the way into Antalya and back without issues. Also you can take the bus from Akdamlar to Antalya (bus 521 or 501 from memory).
As for routes - there are currently somewhere close to 1000 bolted lines within walking distance from the campsites (max 20 min). For sure enough good climbing for a 1 month trip. I climbed solidly 2 days on, one day off for over 3 months and never got bored. However, I do agree with Neil's comment that nearby Kalymnos is better in terms of rock quality. The grading is gernerally softer than the rest of Europe (similar to Kalymnos). Personally, I think the best sectors are 'Sarkit' and 'Trebenna', and the small sector 'Left Cave' has some quality routes.
If you need any more info about my experiences in Geyikbairi or other climbing areas in Europe feel free to PM me. Might be some time replying but I'll get back to you for sure. Enjoy the holiday! Nick