Tires are the cheapest thing to replace, so check the wear. Look at the brake pad wear, not that pads are expensive but to make sure there is some left so they haven't damaged the rotors. If you have a chain-stretch tool (or set of calipers) you could bring that and check the chain as well. If the existing owner has run the chain > 1% "stretch", the next time the chain is replaced you might need to replace the cogs and possible a chain ring or two, which can add up $ fast.