You certainly can go to steam powered.com and download/install the Mac Steam client. If you owned some Windows games that are Steamplay titles, you'll instantly have some stuff you could play natively on your Mac via Steam. For example, COD4 and Civ IV are Steamplay titles. So if you own them on Steam for Windows, you also own them on Steam for Mac. The original Borderlands is available for Mac on the Mac App Store as are many other good games. Do a search there for "Feral Interactive" and also "Aspyr Media." These are both companies that do excellent ports of Windows games to Mac OS X. You'll find lots of good stuff just checking them out. And of course, Steam have over a thousand Mac titles to look into. You can check the Store pages to see what the system requirements are on a per game basis for whatever you are interested in. So make sure your GPU is supported or if it isn't clear ask here about a particular game with your particular graphics chip.
Personally, I like shopping on both the App Store and Steam. I've had good experience with both myself. Amazon is fine too. I got some games there as well. EA's Origin is also available for Mac for a few select titles such as the Sims series, Dragon Age II and some Feral games. Those are all good starting points at the least.
Some will tell you that you need Windows to play games. I disagree and rarely use it myself even though I haven't gotten rid of it yet on my iMac. The only reason to bother with that really is if there is something you really want to play bad enough that isn't on Mac such that you are willing to spend for Windows, set it up and reboot to it whenever you want to play that game. Some folks swear by this as the way to go and others are content to stick to Mac for the most part if not entirely. I fall into the latter camp myself. I have more Mac games than I know what to do with.
Congratulations on your new toy. I hope you enjoy your Mac as much as I do mine.
By the way, if you like Blizzard games, World of Warcraft, StarCraft II and Diablo III are all available for Mac on Blizzards own store and elsewhere. There's really just a ton of good stuff for Mac now. Some of the Total War strategy games are on the Mac App Store: Rome, Empire and Napoleon. I could list all kinds of stuff but you should go have some fun window shopping for yourself. I think you'll be pleasantly surprised to find quite a variety to pick from.
You mentioned Skyrim and that game is not available in a Windows version but people do play it on Macs using something called Wineskin. That's a little involved to learn about but not that bad and it does work well for a lot of games although not all, Windows games I mean. My advice would be save looking into that for a little later and explore the Mac games options first. You can always investigate Wineskin here later on which you could use to play Skyrim, assuming it is okay for your system specs, particularly the graphics chip.
Oh, I forgot to mention where you asked about it, Borderlands 2 (which Aspyr ported) is available on either Steam or the App Store for Mac OS X too. So just go to either place and check out the system requirements to be sure you can run it okay on your particular Mac. Aspyr also ported the most recent Bioshock game (Infinite) to Mac as well and again both places carry it.
