You can stay cheap or affordable in Meran. Just 5 minutes by bike from the station there is the youth hostel just for 22,50 € per Person in a double room. With good breakfast. The city is just round the corner and the church too (you get a free wake up call by nice music (really nice)).
The rooms are mostly calm.
For bycicles there is extra space in the cellar.
The staff is friendly and you get an answer to all your questions.
Wifi is free.