Hey ive been living in Cornwall for 3 years so im pretty well versed now!
All three are great options, but each offers something slightly different.
Falmouth has the best mix of amenities, restaurants, and public transport, making it a solid base with plenty of coastal walks and day-trip options nearby, though it’s one of the busier spots in summer.
Port Isaac is a beautiful, classic Cornish fishing village with fantastic hiking on the South West Coast Path, but it can get crowded and parking is limited and it's also very remote, you have to drive everywhere!
The Lizard is soo dramatic, good walking, and a very slow quieter pace, with just enough cafés and pubs on one hand, you also have to drive a lot here down small narrow lanes but ideal if you’d prefer somewhere more peaceful.
If you’re open to other suggestions, Penzance or St Agnes and Truro are also worth a look for a good balance of charm, amenities, and space to breathe.
My favourite beach in cornwall is Pedn Vounder Beach, you need to go, although i think its shut now??!