Seton sands has a wreck of a boat whose bones stick out at low tide. The beach has lost its major landmark with the power station having been demolished. There's a small harbour near where the power station was which could have some interest. Longniddry Bents the other way; birds at appropriate stages of the tide.
You could go out to Gullane and walk round the sands to North Berwick at all but the highest tides (a good solid 2+ hours), a very worth while walk with any number of opportunities on the way. Back on the bus to Gullane. Or park in North Berwick, walk eastwards on the coastal path round the golf course towards Tantallon Castle. Fantastic views of Bass Rock, as Doug says, but some lovely coloured rocks etc on the way as well. If the tide's reasonably low, keep going further than you might think reasonable, past the few houses in Canty Bay, round the headland under the WW2 fort, and suddenly you get a magic view of Tantallon Castle above you on the cliff. You really can't go any further at this point; if you don't want to return via the cliffs, you can go up through the fields to the road.
Or, drive a bit further east on the road out of North Berwick towards Dunbar, talk the road to Seacliff Beach (it's straight ahead on a right hand bend shortly after passing the Castle). Parking is £2 but you'll probably only see one or two cars and there are great views back to Tantallon, plus a tiny harbour, and rocks galore.
Or Dunbar with Belhaven Beach and its two harbours. Or the lighthouse near Torness Nuclear Power Station. Or St Abbs. Or, or, or...
And that's ignoring the hinterland, and not even touching Edinburgh. East Lothian is FULL of possibilities.
