If you can find an apartment in the downtown area of Somerville, you'd have a decent area, an easy commute to Branchburg, and a bunch of shops, restaurants, etc right outside your door.
Bridgewater is also nice, though it might be hard to find a good apartment for $1200. If you can find one, Bridgewater is also an easy to very easy commute (depending on where in town you're located--it's quite large and spread out), and has the mall, movie theater, nice parks, etc. You may want to check out some of the condo complexes off Milltown Road-not sure how many 1 BRs there are, but I know many people are trying to rent their condos and townhomes, hoping that the market will improve, and biding their time til then.
You may also want to try Raritan (the one in Somerset County)-it's located right next to Bridgewater, but tends to be a bit more affordable, and still very convenient for you-maybe not as "nice" as Bridgewater, but still fine and safe (and it has a fantastic pizza place--DeLucia's, and a great deli--Randazzo's, which IMO are worth checking out if you live in any of these towns!). Raritan would more likely have apartments located in multi-family homes or above shops, I'm not sure how many apartment buildings, if any, are there, if that matters to you.