The National Trust has many beautiful sites in the South West, such as the stunning Lanhydrock House and Gardens and, of course, the infamous St Michael’s Mount. Here’s a link where you can find all SW options:
https://www.nationaltrust.org.uk/days-out/regionsouthwest/cornwall
English Heritage looks after some fantastic places too. Probably the most famous English Heritage site in Cornwall is Tintagel Castle, definitely worth a visit! You could also take a little boat trip in Falmouth from Pendennis Castle over to St Mawes Castle. There are various options, take a look at this link:
https://www.english-heritage.org.uk/visit/inspire-me/travel-guides/a-weekend-in-cornwall/
Here is a great link to browse through for many other ideas of places to visit whilst you are in Cornwall (courtesy of Cornwall Online):
Finally, here is a great link where you can find out what events are taking place over the specific dates you are here, courtesy of Visit Cornwall. To quote from their home page:
“There’s always something happening in Cornwall. From food and drink, music, literature, walking, theatre, arts and craft, seasonal fun, anything and everything goes in Cornwall and our What’s On pages are guaranteed to have an event suitable for all. Come and mingle, get stuck in or simply soak up the atmosphere loaded with Cornish culture. Join the locals at an annual festival, dance in the streets, eat local food and enjoy yourselves“: