The whole area is a major UK tourist destination and offers much to do and see for all tastes.
Weymouth town is essentially in two towns in one; a traditional trading and fishing port, dating from around 1250, based around a picturesque harbour with it's Tower Bridge style lift bridge which opens every hour, on the half hour, to let out fishing boats from the fishing harbour and yachts from the large marina. There are many good quayside bars serving traditional ales and many serve the deceptively strong local ciders. Good restaurants offering a variety of different cuisines to suite all budgets and including some superb pizza, seafood, traditional wholesome British pub food, steaks, vegetarian, Thai, Chinese, Indian and tapas, and not forgetting several fantastic traditional places serving proper British fish and chips. Many shops together with art and craft galleries and a few interesting second hand and antique shops can be found on both sides of the bridge. The town also boasts several interesting historical museums. The second part of the town is a Georgian seaside holiday town based around the 3 mile long sandy beach on Weymouth bay with it's deckchairs, swimming, seaside postcards, ice-creams and sand castles. It is all explorable on foot and there are frequent busses from by the Academy into Weymouth together with a 30 min foot ferry sailing 4 times a day from Portland harbour to Weymouth Quay.
Across the bridge, on the South side of the town there is a walk ending in at a pier. Nearby is the Nothe Fort, a 19th century fort built to defend the town, and which is now a museum, The town is also the home of the largest class of RNLI Lifeboats, the Severn Class and this can be seen at close quarters moored on this side of the river.
The Academy itself is actually on the Isle of Portland, on the site of an old Royal Naval air station. Portland is joined to the mainland by a remarkable geographical feature, the UNESCO World Heritage site of Chesil Beach. This is a huge stretch of shingle beach running 18 miles, that has built up naturally to some 50ft high and 600ft wide, by the large Atlantic waves crashing on its West facing shore. It can be seen most spectacularly from either Abbotsbury at its North end, or from Portland the Southern end. An expert can tell where they are along the beach by the size of the pebbles apparently. Behind this beach is the Fleet, a long thin stretch of tidal water famously used in World War II for testing the famous Bouncing Bombs of the Dam-Busters fame. It is said that parts of broken casings can still be found. Meanwhile, out in the harbour itself, a couple of unused sections of the Mulbury D-Day Harbour are still to be seen, just don't sail into them as you will loose. Portland itself is most famous for its Portland Stone, a limestone which was used to build many famous buildings including St' Paul's Cathedral in London and famed for it's carvability. Large parts of the isle are still stone quarries. This gives rise to the taboo in local folk-law of it being bad luck to say the words 'Rabbit' on the isle, as the burrowing of these animals could occasionally cause the quarry face to collapse onto the quarrymen below. At the Southernmost point is Portland Bill, with it's famous lighthouse and cliff edge stone quarries. It is particularly spectacular after high winds. You can sit in the Lobsterpot cafe next door, eating your cream teas, and look out to sea and see the rough tide race just offshore where two tides meet. Boats are advised to keep clear.
Near the centre there are also a variety of eating and drinking places, including the modern bistro, The Boat That Rocks and Cove House Inn which is actually built onto the seawall and offers, alongside it's good food, spectacular sunset views. There is also nearby chandlery, Apollo Marine, where rope, fittings and associated things can be had.
There is a long distance footpath that runs from Poole Harbour around the whole of the Southwest peninsular of England. This runs around the coast and clifftops of Portland and if you have a few hours to spare, and good walking shoes, it is worth the walk as the views are spectacular.
A short drive less than an hour in any direction can take you to any number of interesting and picturesque village pubs, more coastal walks, cider farms, all in areas of outstanding natural beauty. The area is part of the Jurassic Coast, another World Heritage site, featuring cliffs, plants and animals. About 8 miles North of Weymouth is Maiden Castle, the largest Iron Age fort in Europe and its earth ramparts can be clearly seen from the road to Weymouth. Just North of here is the Dorset County Town of Dorchester, good for shopping.
About 20 mins drive from Weymouth is the Worlds largest collection of tanks at the Tank Museum at Bovingdon, next door to the HQ of the Royal Tank Regiment, (where you can regularly expect to see British Army tanks rumbling around the local lanes, so be careful). This museum has nearly 300 vehicles from all over the world including the only working Tiger I tank and the oldest surviving combat tank, the iconic British WWI Mk1. If you grew up making models of these things as a kid, you would not want to miss this place! If you prefer something less 'tanky', Monkey World is also nearby.