Coloma and the Gold Bug are only about 8 or 10 miles apart. If you have several hours, do both.
Coloma is the actual town where the first gold discovery was made. Much of it is re-created, but you’ll see lots of old ruins, building foundations, mining equipment and artifacts sitting around. It isn't just a single museum, although it has a good visitor center with exhibits. It's right on the American River, and there is a re-creation of the mill where Marshall found the little yellow specks. There is a place in town where you can learn to pan for gold. A few years ago, a lesson cost about $7.00 or $8.00, and it isn't over until you've found some flecks of gold along with bits of iron pyrite and red garnet chips, which occur naturally in the area. Then you can cross a bridge over the American River to a bank where the public is allowed to pan.
Gold Bug is a city park in Placerville, and the only city-owned gold mine in the US. There are historic buildings and a hard rock gold mine tour. Panning along river or stream banks is placer mining. The ore has been washed out of its original location (lode) and deposited downstream, where someone like Marshall finds it. "Placer" is the anglicized form of the Spanish word for "place." Hard rock mining is where you get the gold at its source, typically digging or hammering or blasting it out of the earth. For the Gold Bug mine tour, you get a helmet and flashlight and then burrow into the innards of the planet trying to find the "Mother Lode."
All the towns along Hwy 49 are crammed with Gold Rush history. The stretch from Auburn to Placerville (including Coloma) to Sonora is particularly rich with museums, historic sites, and preserved Gold Rush era buildings (many now used as hotels or B&Bs, restaurants, shops, or private homes). My favorite areas are around Sonora, Columbia, Angels Camp, and Murphys. I go to Columbia fairly often, and I almost always go to the museum in the historic town area. The Mother Lode goes all the way to Mariposa if you want to go that far south, and the California State Mining and Mineral Museum is there.
I see that you live in Santa Clara. If you want to make a connection between home and the Mother Lode, take a little afternoon excursion to New Almaden Quicksilver County Park. The connection is that New Almaden was one of the richest mercury (quicksilver) mines in the New World, and mercury was an essential part of refining gold and silver ores in the 19th century. It was extremely nasty and toxic to mine quicksilver and to refine precious metal ores with it, but people did it because of the promise of riches. The Almaden museum is open only on weekends, but it does a great job of portraying the history and how it ties in with gold or silver mining. The park itself is open daily, and you can walk around the old town and see historic buildings or hike in the park and see some of the old mining structures. The toxic waste issues have been addressed, but it’s still not a good idea to eat the dirt there, or to eat fish caught in the reservoir.