West coast of Portugal south of Lisbon

First thing to do: omit this (for too many reasons to list):

Tarifa - Tanger- Gibralter

Next....you describe the trip as "1st weeks of April"...but it's hard to make good choices until you get more specific. How many actual, usable, full days on the ground will you have (not counting the day you arrive or the day you depart)? Without knowing that number, it's really difficult to offer good specific advice for an itinerary (and it's also really easy to set yourself up for an unrealistic itinerary that will not result in an enjoyable trip).

The area you describe is not some empty, quiet, undiscovered backwater. It gets plenty of tourism. Sure, there are some places that are relatively more and less "touristed" than others, but it's not lacking in attention from other visitors.

Finally, calibrate your expectations based on the weather: if you are looking for beach time, the first week of April may not be as warm and sunny as you hope. Again, if you better define the specific dates of your trip, it will help set expectations for what kind of weather is likely.

Don't worry about the fact that you do not speak Portuguese. Have you been to Europe before, or will this be your first trip?

As for places to go (and lots of other practical suggestions), have a look here - lots of useful info on Portugal:
Rick Steves Europe > Explore Europe > Portugal

I can't speak to how touristy the coast will be in April, but if you avoid the weekends there that should help a lot. I only visited Nazare this summer and it didn't have much to offer in my opinion except tons of people squished into a tiny town on the beach with not very interesting food options. Not to say it was terrible, but it's a town that caters to thousands of people, locals and tourists, that all want to go to the beach. If that's what you're looking for, it has it. It doesn't have much else. You could try other coastal towns like Peniche, Sao Martinho do Porto, Figueira da Foz and Aveiro (which is on a bay, not the ocean). Not speaking Portuguese won't be a problem. Everyone speaks some English. I would focus on Lisbon, Sintra (also check out Cabo da Roca while there) and Porto, those are the highlights of Portugal. Coimbra is worth a stop as well, it just depends on how much time you have.

Early April isn’t likely to be beach weather anywhere in Portugal.

There is more to see between Lisbon and Porto (Alcobaca, Tomar, Batalha, Coimbra, Obidos etc) than the area south of Lisbon IMO. I stayed near Caldas da Rainha to cover these towns (not Coimbra), which was near the coast at Foz do Arelho. Nazare isn’t my favourite coastal destination.

I have also stayed near Melides, about 1.5 hours south of Lisbon. It was a good base to see Comporta and other more low key local towns plus some lovely beaches and walking, but I was there early June when the weather is much better than April. Some locals didn’t speak English and menus were in Portuguese only, but I have been to Portugal enough times to negotiate my way round a menu so it wasn’t an issue. The towns north of Lisbon were more interesting IMO.

Thanks All-
David specific dates are fluid but I was trying to take advantage of a 'shoulder season' and my son's spring break. I have looked at March 24th- April 8. I plan for a full 13-14 days on the ground. We did a similar length trip to Munich and several spots in the Swiss alps a few years ago... but not with the kiddo. I'm ok with it not being full on beach weather but I do love exploring the cliffs, beaches, and food/culture.

If that time of year is really advised against I can shift to when my son is out of school but I wanted to avoid the highest cost and number of people:) Our travel style is trying to find the best off the beaten path local spots while soaking in the history and highlights that are must see...That's to say we usually don't stay in hotels and typically skip tour groups... I'm guessing that's what many of the folks in this forum do.