cynthia,
My suggestion would be to stay in one of the five towns. I really enjoy the ambiance and scenery of the towns in the evenings especially. Early April may not be too crowded although that will depend to some extent on the cruise ship schedules. The water in that area may be a bit "cool" for swimming.
I've never stayed in Lerici but would not suggest Porto Venere as it's not the most convenient location for getting to so it would be a hassle for day trips. As someone mentioned earlier, there's no rail access so that means a bus trip to La Spezia before you can access rail. While the boats do go to Porto Venere, they don't run in inclement weather and the schedules aren't as frequent.
Everyone here has a preference for towns, and I always prefer to stay in Monterosso. It's the largest of the five towns and therefore has the greatest number of lodgings, restaurants and other tourist amenities. The town has two parts, a "new town" and an "old town" so seems to absorb crowds better.
I'm usually travelling solo so don't use Air BnB. I have a favourite hotel in Monterosso and can't imagine staying anywhere else.