Catholic is definitley not in the suburbs. It's not right "downtown" - i.e. Capitol Hill, but few things are except for gov't buildings, monuments, and businesses.
Catholic is in Northeast DC, which is not the nicest area of DC but not the very worst. It's on a metro stop and you'd need to drive or metro to the nicer places in DC, such as Adam's Morgan, U-Street, or Dupont Circle, which are where you'll find the good restaurants, shopping, bars, and clubs.