Pulling from your other posts, given that you're fresh out of college, this probably represents a significant portion (if not all) of your current savings? Two things you should do with it: first and foremost, KEEP IT. This $6k can be the beginnings of a solid emergency fund for yourself, so that you won't find yourself in a tough spot later on if something unexpected happens. Typically it's recommended to have at least 6 months' expenses in an EF, but you have to start somewhere, and can build up your EF over time.
Second (and this is up to you), you can look at finding a slightly better yield elsewhere. However, as your EF, you want to keep it in cash (savings account, Certificates of Deposit (CD's), or a money market account). Keeping it liquid is more important than getting a good rate, but a better rate is always nice. Now, are you getting .35% quarterly (thus 1.4% annually), or are you getting .35% per year? Normally, interest rates are expressed per year, as a % APY. If you're getting 1.4% per year, you probably can leave it where you have it, because you're not going to get much better right now. If you're getting .35%/year, you can look into an online savings account, most of which right now are offering between 1.0% - 1.5%. You can look at
Ally,
ING, or a number of other places. There's a list of other options
here. Otherwise, just keep saving! The how is not nearly so important as the doing.