Not too much really exciting close to Bozeman. Flathead Pass makes a fun drive but not really wheeling in my book unless you want to do it with 4' of snow. A lot of nice trails in the Tobacco Roots about 30 wiles west of Bozeman.
Below is a little blurb I put together on the Tobacco Roots.
Here are a few of my Tobacco Root Mountains favorites that are close to home:
South Meadow Creek, FS 1221. N45° 27.606', W111° 52.188' McAllister access. My stock JK Rubicon has no problems with it, but a couple of spots you need to pick the line well. Piece of cake for the 3B on 33's. Another trail (6361) branches to the north after the Missouri/McKee mine/mill and tops out on the ridge at South Baldy Mountain (10,105') with a loop option to take Trail 6362 back to the Washington Creek Road.
South Meadow Lake
North Meadow Creek, FS 965/6338/6340. N45° 30.817', W111° 47.579' McAllister access or take Warm Springs Creek road over the Revenue Flats from Norris. You might get a stock JK/TJ up these but highly likely they will not look too good after the run. Lots of boulders and tight spots and I'm going to say lockers and/or winch necessary but rewards are some great scenery. Lakes include Upper and Lower Twin Lakes, McKelvey, Cliff, Mine (on some maps Alpine), and Kid Lakes.
Lower Twin Lake
N. Meadow to S. Willow Creek, FS160, N45° 32.174', W111° 52.110' McAllister access. Only a couple miles of real Jeep trail-very steep and can get pretty muddy. A lot of gravel and semi-Jeep road on both ends.
South Boulder River, FS 107. N45° 48.187', W111° 55.570' Cardwell access. Twenty something miles of gravel with about 4 miles good Jeep trail to Sailor Lake trail head (1/4 mile hike to lake-Trail 7140, another 1/4 mile hike to Globe Lake, and maybe 1.5 mile hike (Trail 7167) to Brannan Lakes. Hiking access to Louise, Curly and Lost Cabin Lakes also off this road. Road passes through the old Mining town of Mammoth.
Upper and Lower Brannan Lakes
Wisconsin Creek/Noble Fork, FS 6370/8300/6015. N45° 27.585', W112° 11.836' Sheridan access. Another very scenic area with several lakes, including Crystal, Jackson, Sunrise, Noble, and Blossom. The only one you can directly drive to is Noble Lake. Stock Jeep can probably make all trails but some of the Noble Fork trail where a little more clearence is highly desirable.
Dry Boulder Creek/Boulder Lakes, FS 1007. N45° 35.845', W112° 14.832' Twin Bridges access. Cake walk into lower Boulder Lake but trail from Lower to Upper Boulder Lake has a couple shelfs where you will want lockers on both ends or you will be running line.
Upper Boulder Lake
Indian Creek, FS 158. N45° 27.606', W112° 09.853' Sheridan access. Not too challanging but again, nice scenery. Used to be able to drive into Rossiter Lake but FS rebuilt the last 3 to 4 miles of trail for hiking only. Hill Reservoir (breached?-have seen no water in it for a number of years), Taylor Lake (swamp), Oval and Triangle Lakes (both small but nice) also up this drainage.
Pony/Windy Pass/N. Willow/Cataract Creek. N45° 39.540', W111° 54.232' Many, many prospects and old mines, along with several remains of small mills. Some of this burned summer 2012 and I am not sure what is now open. Cataract Lake is a drive to, Upper and Lower Mason Lakes not much of a hike, but not much for lakes either.
Upper Mason Lake
A word of caution: if you are camping in the Tobacco Roots, pay attention to the FS bear requirements. We came face to face with a grizzly sow and 2 cubs a year back. That encounter turned out well for all participants but could have been really ugly. And it was a little costly. Bought a S&W 500 to replace the 44 mag after that incident.
And I don't think flat fenders will be a problem around here. There are regs to have wheels covered but essentially no enforcement unless something is really obnoxious.