The San Juan Mountains around Silverton often have lots of snow in May and even into June. If the Silver Lake you are talking about is the one above Silverton, I'd be more than a little cautious about trying to get there that early in the year. Arrastra Gulch has lots of steep potential avalanche chutes it that is the way you are thinking about. If you're thinking taking the Kendall Mountain road and going up and over the ridge and dropping into Silver Lake, there's probably less avalanche issues, but I don't know how far up the road might be open that early. Dropping into the basin might be a fun slide, but make sure you're properly outfitted so you can kick your way back up the snow.
Besides Mesa Verde NP, check out the
Anasazi Heritage Center near Dolores. Interesting museum and they can lead you to other, smaller sites that Mesa Verde (which will be limited because of the early season and possibly snow on some trails). Hovenweep in Utah is worth the drive if Mesa Verde is too snowy.
If you have some specific 4x4 trail in mind, go to
this website. Scroll down to find the road you are interested in and you'll get an idea as to when things open up. You can also look back several years.
I think two days in Gunnison would be enough that time of year. It's cool there even in the middle of summer. Virtually no 4x4 roads will be open. Even Kebler Pass will probably still be closed. Take that extra day and add it to Durango or Salida.
Instead of Buena Vista, I'd look into staying in Salida. More restaurants, many interesting art galleries featuring works by local artists. Plus, it's lower in elevation and warmer if you're just walking around town. More motel options also. Several hot springs along the west side of the Arkansas River Valley, like Cottonwood and Mt Princeton. Never been to any of them, but just driving by, I'd probably opt for Mt. Princeton. You might be able to drive up to the ghost town of St. Elmo and poke around there. Worth the drive. As noted, the mining museum in Leadville is interesting. Good option if the weather is iffy. If you're looking for another train option, there's the
Royal Gorge Train. Not steam, but an interesting trip in the bottom of the canyon.