As far is IN Austin proper, there are a few fields, but all are more suited for the rec crowd and a bit on the pricier side. Google around and you'll find em (Outlaw, TXPB, Austin Paintball, etc).
The closest fields I would suggest and with the most tournament/speedball action with competition are...
XFactor Paintball (60 miles south in San Antonio) - http://www.xfactorpaintballpark.com
Comanche Badlanz (70 miles north in Killeen area) - http://www.comanchebadlanzpaintball.com/
Both of these places you are looking at about $50-65 for paint and field fees. Both fields are field paint only. They both have a proshop with a limited selection. Not sure if either have gun techs onsite.
As far as tournaments to go watch, there are a few regional series / leagues this year - AES Series, CTPL, and AXBL. Look them up on APPA (paintball-players.org) for the next date/location.