Many thanks for all the replies and apologies for my delayed reply.
I hope for my trip to be sometime during July, August or September (at the latest). Not sure yet on how long I am going to stay in Penzance - this depends on how much money I can raise and the cost of travel and accommodation.
My main reason for the trip is to travel on the Night Riviera sleeper and hopefully returning first class on an HST - neither on which I have ever travelled on.
I've been planning a trip on one of the sleepers for this summer and I have decided on the Night Riviera due to my love of Cornwall.
Originally, I thought about travelling down to Penzance on the sleeper and then returning the same day but this seems like a tremendous waste and I was wondering where I could leave any luggage whilst I explored Penzance, so therefore I have decided to stay for a least one night, possibly longer, before returning.
Unfortunately, my budget is a little bit restricted - I'm aware that Cornwall can be an expensive place to visit and I am hoping to get an idea of how much I need to save up. I usually pay around £35 per night B&B, but that's in Lincolnshire, which I appreciate is a bit different to Cornwall
The Mount Haven hotel looks really nice but sadly might be beyond my budget on this occasion but will be noted for a future visit. Sorry, I should have said that my budget is "fairly" limited

I have very roughly estimated about £200-£300 for the train tickets.
Is there anywhere like Premier Inn, Travelodge, or Holiday Inn in Penzance? If not, I will probably choose a B&B, possibly with evening meal.
Food-wise - the Penzance Meadery is definitely being considered - thanks, richw - and pasties and clotted cream are very much on the agenda
Unfortunately, I am reliant on public transport - what are the regular rail / bus services like to/from Penzance? Had a bit of a shock the last time I stayed in Lincolnshire when I'm used to buses every few minutes! Tried to get from Market Rasen station to Louth to visit a relative when there is only one bus a day!
I have been fortunate to visit Cornwall twice before with my parents by car, but not by train yet. We visited Padstow, Newquay, Mevagissey and St. Austell and Fowey amongst other places - the furthest "south" I've been so far is Newquay.
Would love to visit the Scillies at some point too, but not sure if I can stretch to that on this occasion.
Considering that I will be walking or using local transport would Marazion, Newlyn, Hayle, Mousehoule, Porthcurno etc. be within walking distance or do they have usable transport? How do the above compare to Padstow, Mevagissey and Fowey?
Apologies for the long post and thanks again.