There is a lot of good rivers and stream fishing available within an hour of Helena. I spent 4 years living in Boulder (30 miles south of Helena) and althought the Missouri is one of my favorite rivers for trout, in June the water can be high making it tough to fish without floating. The Smith is problamatic for access, unless you can float the canyon from near White Sulfer Springs downstream. The lower Smith is also problamatic for access because many of the ranchers have had problems with folks from Malstrom Airforce Base and yahoos from Great Falls littering and leaving fences open allowing cattle to get out.
At the risk of getting some of the locals miffed because some of these are sleepers the locals keep quite about due to there small size, I'll list quite a few other for you. Prickly Pear Creek (near the town of Wolf Creek north of Helena), Little Prickly Pear Creek (south of Helena near Montana City), Little Blackfoot River (west of Helena on Hwy 12 just over the pass), Boulder River (south of Helena near Boulder, MT), Jefferson River (south of Helena to Boulder, get off and go south to Cardwall, could be high in June), Clark Fork River at Garrison Junction (west of Helena were I-90 and Hwy 12 meet), Blackfoot River (northwest of Helena near Lincoln, MT), 16 Mile Creek (south east of Helena toward Bozeman), Lower Galatin River (south east of helena near Manhattan, MT), and Lower Madison are all within an hour's drive of Helena.
If you move out to 2 hours of Helena, Sun River above the town of Sun River (north of Helena), Dearborn River (north of Helena, but access is problamatic unless you can float it), the Yellowstone at Livingston, Upper Gallatin, Madison near Ennis, MT, Ruby near Sheridan, MT, Big Hole (near Divide and Melrose) Beaverhead (near Dillon), and upper Clark Fork (from Milltown all the way up to Warm Springs) are available.
Helena is a great place to use as a jumping off point for fishing in Montana.