I'd do 2 and 2. The Park is just not to be missed, and while a day trip from Breck wouldn't be impossible, it isn't really ideal. From Breckenridge I would plan a day out Aspen way. It's about a 2 hour drive but there are some things to see along the way.

So 2 days in Breckenridge - one day of hiking in Breckenridge, and the other day driving around.

You think I should do the loop that fmpden mentioned - out to Glenwood Springs, down to Aspen and Leadville and then back to Breckenridge - or is that too much for one day?

If you want to do a driving trip from Breckenridge, I'd suggest going through Glenwood to Aspen, and back. I wouldn't spend extra time to see Leadville, because Aspen is much better IMHO.

Another day, I'd drive the pass above Breckenridge and explore that direction.

Again, I'd prefer to spend all 4 nights in Breckenridge to allow for some non-driving days, too.