Britannia's Inn is the weatherspoons near the ground. Avoid the cherry tree as it's home only.
Barbican or Union Street are the best bets.
Other options are The Barcode, but that's all the chains, turtle Bay, cosy club, brewdog etc Or The Royal William Yard.
Barbican pasta bar and The Harbour seafood restaurant are 2 places I recommend on Southside Street (barbican) or The Leandra by the market in Frankfort Gate