From Imst for sport climbing you have Ötztal (gneiss) and Nassereith (lime) right next door. Both very well documented on
http://climbers-paradise.com
In Otztal I've climbed at Oberried - cute, pleasant enough climbing but laughably short routes - and Nößlach - has some good-looking multipitch routes but they were wet, wasn't that taken with the single pitch stuff. At Nassereith I've only done some of the multipitch routes: very mediocre, the single pitch stuff may be better.
Martinswand near Innsbruck: the sport climbing I've done there was hideously polished and crap, the harder stuff may be better. Some decent-looking multipitch.
Maybe also check out
http://bergprofi.com/ for some good-looking multipitch stuff around Ehrwald - slightly further away, about an hour's drive from Imst. Or Leutasch: Chinesische Mauer for sport, bigger mountain routes higher up the hill on the south side of the Wetterstein