April and May are probably your best bet if you want quality without breaking the bank. The weather is still pleasant, the beaches are less crowded, and flights drop significantly once high season ends. The trails are great during this time because it's not too hot for hiking, and rainfall is more predictable than during winter months.
Now, there's something people usually overlook: September and October might look good on paper (spring, moderate prices), but the weather down south is pretty unstable. You'll get beautiful days mixed with heavy rain and wind that can wreck beach plans out of nowhere. If the goal is really to enjoy the beaches without stress, April-May or even March still make more sense.
December through February really do have perfect beach weather, but beyond the crowds and high prices that were already mentioned, there's the parks situation too - some get packed with tourists and you end up spending more time standing in lines than actually enjoying yourself. If you can be flexible with your vacation dates, don't fall into that trap.