The train station in Bolzano is not far from the historic district, and there are certainly hotels within reasonable walking distance. Or you could hop in one of the taxis that always seemed to be waiting outside the station (this will be true in any European city of size).
I don't often recommend hotels on this forum because I'm cheap, and most American travelers are looking for something a bit more upscale. But in the case of Bolzano, I ended up getting a bargain deal at the Parkhotel Laurin, which I have no hesitancy in recommending. There are certainly less expensive options in Bolzano, but many are not air conditioned. That might not be an issue in September (particularly if you hit Bolzano quite late in the month), but I can tell you that in the summer, Bolzano and the other towns down in the valley can be miserable if you have no air conditioning.
Here's the map of Bolzano from Google Maps (always a good resource). You may need to zoom in with the "+" symbol. The train station is marked with a small aqua icon. See that cluster of light-gray lines? Those are the rail lines. The Hotel Regina is right at the station, and the Parkhotel Laurin is a few blocks away, just beyond the park. The lovely historic district is the sort of peach-colored area beyond the Laurin. Lots of hotel options scattered around.
To get to the Val Gardena, you would first take a bus (departure point is somewhere near the train station), then you might take a lift to get up higher. I didn't buy advance tickets for either the buses or the lifts, just walked right up. The tourist office in Bolzano usually has a booklet with all the local train, bus and lift schedules. It is very handy for seeing what your options are. According to Google, the T.O. is near the intersection of Via Alto Adige and Via Marconi/Via Garibaldi--exit the train station and walk along the main road to the left.
How much time you need in the area depends on what you want to see and do. I would consider 3 nights the minimum--one day for Bolzano and one for the mountains. If you want more mountain time than that, I'd agree with the others here (who will probably comment soon!) that it would be better to stay up in the mountains in a place like Ortisei. The bus goes to Ortisei, so you would not be hauling your luggage onto a lift.
Incidentally, there is a small lift you can get right from Bolzano, along the Via Renon. It's not a substitute for going up to the Val Gardena, but if you have a few extra hours one day, it's a pleasant diversion.
Edited to add:
To see the train schedules between Bolzano and Lake Como, you'll need to specify a town. You can use the TrenItalia website (which will also display fares) or the Deutsche Bahn website (no fares shown for non-German trains). I find the DB site easier to use; TrenItalia insists that you use the Italian spelling of all station names.
You will be changing trains in Verona and in Milan. I recommend avoiding the itineraries that require you to change trains in two different Milan stations. Part of the trip will likely be on a fast train, a Freccia, so the overall ticket price will vary, depending on when you buy the ticket. Buy earlier and commit to a specific train (no changes or refunds) and you'll save quite a bit of money. Wait to buy till shortly before your travel date and you'll pay more. It appears that the trip to the town of Como takes between 4 and 5 hours; you will probably be going farther and might need to take a boat. The rail cost is up to about €50 per person one way. I don't know what a typical buy-in-advance fare would be. I'd guess perhaps €25 or so.
