The Denver area is pretty pricey these days, but some of its suburbs aren't too bad, or since you're single you might be able to find a decently cheap roommate situation.
We have the Avalanche (hockey), Broncos (football), Rockies (baseball), Mammoth (indoor lacrosse), Outlaws (outdoor lacrosse), Rapids (soccer), Nuggets (basketball) and some other minor-league types. A new lightrail line goes from downtown to Denver International Airport, so you might even be able to go carless, if you really want. The mountains are great, but a lot of people are here because of the mountains (ski traffic in winter is notorious).
Cost of rent/housing is the only hiccup, though, you really have to get a little lucky to find a cheap living situation, but that's from my frame of reference, so YMMV. Nothing else is particularly expensive.
I am seeking a city on the coast
Oops, just reread this. Oh, well, I'd still argue Denver is otherwise a good choice. I don't know what the m/f ratio is, but you will find lots of active women here :)
State income tax is booked at 4.63%, really not too bad. There was an initiative to create tiers, but nobody was having any of that crap.