Baker's Hole is located very close to West Yellowstone. This is both a pro and a con -- pro, as it allows you to zip into town if you need some groceries, want to grab a pizza, etc. You can literally be in town in 3 minutes. 
The "con" side is that the main road into West is VERY close to many sites within the campground, and the road noise is pretty constant. We had a last minute trip and scored Site #16 (Electric) and while the site itself is great (timbered shade, roomy parking spot for the camper, hammock-friendly trees, food lock box, etc.) it is literally 40-50 yards from the road. 

At one point, about 30 Harley's roared by, and I couldn't hear my wife talking to me at the picnic table. Not good…..But, that is the deal if you land in one of the spots nearest the road. 

My advice (and plan next time) is to get there early (it is first come/first serve, no reservations) and head directly to the spots closest to the river. Not only does that put you within 10 seconds of fishing, they were a fair bit quieter than those near the road. 

The camp hosts check in and drive around in their golf cart frequently, taking care of the place. They do a great job. 

All in all, I would recommend this campground, as you have easy access to fishing the Madison, a quick trip to West Yellowstone if needed, or to start a trip in Yellowstone Park. 

A few tips:

- Bring bug spray and a citronella candle/Thermacell, etc. anytime in the summer. The mosquitoes can be really bad. 

- Bring a hammock; great trees to sling one up can be found at almost every site

- Bring your flyrod! 

- Bring bear spray, and be diligent about food prep and storage. This is grizzly country.

Family and I stayed here in late May for three days. We have stayed in the past in June and July as well. 

Campground is south of Big Sky, so if you need to buzz into town for any last minute supplies, it is only about 10 minutes up the road and has everything you could want. 

Campground has both standard and electric sites. We have a small camper and scored one of the spots near the south end, which is also close to the Elkhorn Creek Trailhead. Best sites are obviously closer to the river, with those at the far north end or south end the best options. Some of the southern end options on the east side of the campground road are tucked up pretty tight to the hillside, and are not as desirable of a location. 

Pros:
Beautiful setting, easy access to hiking, cave exploration and rock climbing.

Later in the summer, the Gallatin river provides good fishing opportunities. 

Yellowstone Park is about 40 minutes away. Tons of hiking options within Gallatin Canyon, all accessible via a short drive if you want something away from the campground. 

Great camp hosts, who check in with everyone, have firewood, and ensure everything is good to go. 

Potable water spigot, bear proof dumpster and recycling are all available near the entrance. 

Cons:
Being that the campground is near the river, which also parallels the highway, road noise is pretty common -- big semi-trucks hitting the rumble strips take something away from the peaceful setting, but it is not a deal breaker. That really is the only minor gripe. 

Highly recommended overall for tent or RV camping.