I am somewhat biased as I have lived here all my life and have seen Weymouth deteriorate.
Had a quick look at the guest house website and they have car parking which is now very important in Weymouth.
You are not far from the beach probably about 100m, and depending on the weather you can walk right along to the sands or left back up to Greenhill. However don't leave valuables on the beach whilst you are in the water.
Bring plenty of cash for car parking but remember not to leave anything that looks valuable in view!
Natural sites: Portland Bill, Chesil Beach, Abbotsbury Hill, Cerne Giant, Maiden Castle.
There is Abbotsbury Swannery, The great Maize maze if it is still standing, Tank Museum at Bovington, Monkey World.
The Weymouth live music scene is still vibrant. Many of the local pubs have bands on during the evenings, which cover for most tastes from 60s covers to heavy heavy metal. We do have a couple of night clubs and even a lap dancing club.
There are amusement arcades along the front. If you fancy a long evening stroll you can walk past Greenhill along the Preston Beach Wall and along the beach to Bowleaze Cove where there is an amusement complex, go karts (and a pub) etc. Probably about 3 miles there and back (maybe 4).
The Dorchester County Show is on one weekend in early September which may make a pleasant change for a saturday or sunday..
The town is at the other end of the Esplanade, not worth driving as you are probably parked as close at you can get!
At the far end of the beach is the Pavilion which may have a suitable show on for a night's entertainment.
What sort of stuff interests you?