New to the whole biking business

I am going to be in Austria for a year and I would like to do some touring on a bike. Which trails are good? I will be based in Innsbruck and anyone has any idea where I can get a good bike in Innsbruck? I realised that bikes are rather expensive so is it advisable to fork out more euros for a better bike or just go for the cheapest as I think I will not be biking place to place but more like biking in and around various cities.