The Brass n Granite in Grange Street is about a 5-10 min walk to the ground, you'll also pass the Portmann Hotel on Portland Road on the way or you've got the Park Hotel at Rugby Park, nice but not the cheapest....
You can park on the side streets, depending on arrival time before kick off, but not where its coned off or you'll get done. There is plenty of parking around Glencairn Square about a 10-15 min walk to the ground, thou its the opposite side of the ground from the pubs mentioned.