Would Mondello be a good base for visiting Palermo in April? I believe there is an easy bus connection into the city and also to the airport. Trying real hard to avoid staying right in the city. But then again, should I?
This web page shows the route for the 806 bus. It appears that the entire run of the bus takes 35 minutes to Piazza Sturzo. That's not bad at all, but of course you'd need to add the time to get to the places you want to see, either from that stop or from some other that might be more convenient.
I haven't been to Mondello, so I have no opinion about its desirability as a base, and I have no idea what it might be like in April. I enjoyed staying right in Palermo (which had a lot of sightseeing targets I was interested in), but I am a big-city person and don't care about beaches.
Why are you trying to avoid staying in Palermo? If it's because you'll have a car you plan to use before and after visiting Palermo, that's one thing. If it's because you think Palermo is gritty or unsafe, my experience suggests that perception is outdated. I've stayed in Palermo twice and found the city center lively and easy to navigate.
I am probably in the minority, but although I love Sicily, I do not like Palermo. When I was there a few years ago I saw two dead cats just lying in the streets and this was near the historic city center. I remember liking a small chapel with beautiful mosaics, but can't remember another thing I enjoyed. For me a day trip would be more than enough.
When we visited Sicily last April, we were also leery of Palermo and considered staying in Mondello. Instead we stayed at B&B Delle Vittorie in the heart of the historic district and were so glad we did.
Palermo is busy and crowded but also vibrant and interesting, with great sights everywhere you look. Several of the main streets have been pedestrianized, including Via Maqueda, where our B&b was located. So we could just step out our door and immerse ourselves in the city without worrying about traffic or bus schedules.
I was in Palermo in the late fall of 2017 and really enjoyed the city.
If you don’t have a car, you should stay in Palermo.
Although Mondello is a very pleasant beach resort town (or more precisely “city district”, since it is part of the city of Palermo) however I would imagine that it wouldn’t be as vibrant in April, unless maybe on a warm weekend (I’ve been there only in May and June).
If you have a car and using Mondello as a staging point for out of town day trips, then I can understand not wanting to drive into Palermo, which is a traffic nightmare.
If your fear is crime, then it is not justified. Palermo is now the safest large city in Italy.