Can Elder Dragon target an enemy base? Or only battlefield?

Yes — an enemy Base is a location, so Elder Dragon can target enemy units there.

Per Rule 107.1.b, each Base is a Location. Elder Dragon's play effect says "choose up to one enemy unit at each location" — which covers both battlefields and bases (and every other location on the board). So when you play Elder Dragon, you can choose up to one enemy unit at your opponent's Base, plus up to one at each battlefield, plus up to one at your own Base (if an enemy unit is there).