Merced Grove is a nice 1/2 day trip, but you might enjoy Tuolumne Grove more. It's a bit larger and easier to reach as the "trail" (really a segment of the Old Big Oak Flat Road that was closed to autos in 1990) is paved, plus it's a shorter distance.
On the other hand, if solitude is what you're after, Merced Grove is the one. The first part of the trail uses a dirt fire road of relatively recent vintage. Where you meet the Old Coulterville Road (about 3/4 mile from Highway 120), you follow it downhill to the grove. This was the first road built into Yosemite, and it's showing its age -- this part of it has been closed to auto traffic since the early 1950s and was never paved, so it's a bit more of a difficult hike than the one into Tuolumne Grove. There's a ranger station in the grove and it's an impressive sight seeing all these mammoths towering over you. When I was last there (late afternoon), i had it to myself. But judging from the often crowded parking lot at the trailhead, it's a fairly popular hike, so it may be much busier in the morning/midday.