There is just a few backpackers accommodations in Nusa Penida all located on the north side of the island (at the west & east tips) : opposite to the Manta Bay & Manta Point dive sites. There is one dive center on the island, I do not feel comfortable to recommend.
Nusa Lembongan is much more developed for tourism (plenty of accommodations, totally uncontrolled development rate, ...) with 12 dive ops on the island.
Actually getting to Manta Point / Manta Bay dive sites takes less time from Nusa Lembongan than from Nusa Penida north coast.
Still you can stay in Bali : Sanur or Padangbai being the closest area to get to Nusa Penida.
I would personally recommend the second one, less crowded and sea conditions tend to make the trip to Nusa Penida faster.