I lived in Denver for years but no longer do, so I can't comment on current conditions. Generally though, it's too early in the season for driving up mountains. You can check the websites for both Pike Peaks and Rocky Mountain National Park to see what's open and what's closed. Additionally, a day trip west on I-70 is very scenic even if you don't end up going up any mountains. A popular weekend drive for us would be to take the highway as far as Idaho Springs, hang out there for a bit, and then drive back.
I also recommend Garden of the Gods in Colorado Springs, and closer to Denver, South Valley Park, Roxborough, and other places have the same red rocks type scenery, although not on the scale of Garden of the Gods. I would also recommend looking into the various parks in the Jefferson County Open Space system as all offer nice scenery within an hour's drive of Denver.
As for Denver itself, it's light on sites, with your best bets being the mint, the art museum, and the botanical gardens. Restaurants and coffee shops come and go and I'm 8 years away from my time there so I'll leave those recommendations mostly to someone else. However, definitely check out The Buckhorn Exchange for its old west feel. Also, I still dream about the pizza at Blue Pan Pizza. TONS of breweries and brewpubs though if you like craft beer.