Well Falmouth itself is no surfing Mecca however you're in the right county.
Most reliable swell is north coast so for you from Gwithian area up to and Newquay/Watergate depending how far you want/ need to travel.
After that south coast for Praa and spots on the Lizard are nice although tend to be covey rather than open beaches.
Falmouth does go off occasionally but mainly in winter on v.large westerlies or some wind swell whips things up too.
As mentioned there are no motorways in Cornwall so you're fine- access wise is fine, loads of car parks, loads of variety, just a bit of distance!
I won't put a scale on it as some guys on here will do 4/5 hour road trips to North Devon and think that's fine- I get annoyed with 12 mile hike to northcoast or 5 to the south so it's all about perception.
Three most important things in life: Surf, surf and surf!