I live between Weymouth and Dorchester and feel I have the best of both worlds! It is on the train line with South West train line going to London Waterloo and Great Western Trains going to Bath, Bristol, Gloucester etc. The local train stations are Weymouth, Upwey - free station parking, Dorchester South and Dorchester West.
There is a thriving large outside and partially covered market every Wednesday in Dorchester opposite Brewery Square.
Shopping in both towns has been badly affected in the economic downturn with stores closing down and too many charity shops...but there is a mix of chain and independent shops...Dorchester has ‘naice’ shops like Phase 8, Joules, Crew, some posh art gallery shops and a nice department store (in two locations) called Goulds with their garden centre in Weymouth. Also shops like Fatface...sadly Laura Ashley recently closed. I love the old Curiosity warehouse selling antiques/recycled items on the outskirts of town.
Obviously this year has been a disaster for the arts but Dorchester does usually have a thriving arts scene, not just in the town eg. The Corn Exchange but in the surrounding villages.
www.dorchesterarts.org.uk
Dorset & South West: www.artuk.org
www.sculpturebythelakes.co.uk (beautiful)
Dorchester also has an Odeon and a lovely independent cinema:
www.plazadorchester.com
Weymouth has the Pavilion Theatre (great for pantomimes!) and a Cineworld cinema. Lots of festivals in the Summer eg. The Nyetimber Seafood Festival (cancelled this year), fireworks on the beach (not this year) and apparently the huge carnival is due to return in 2021. Lulworth is only a 25 minute drive away where Camp Bestival is held. Sadly all the country shows were cancelled this year.
www.dorsetseafood.co.uk
www.weymouthpavilion.com
www.visit-Dorset.com
The National Trust has places in the local area eg. The Hardy Monument, Thomas Hardy house (Max Gate) and the Thomas Hardy cottage plus of course the coast...Ringstead Bay and the cliffside walks on the south west coastal path. Around here it is designated an AONB (Area of Outstanding Natural Beauty).
I don’t have kids in schools but I understand that the Thomas Hardye school (state school) in Dorchester is excellent and there is a bus from Weymouth which goes there. There is also a Catholic school in Dorchester which has pupils from Weymouth.
Property prices are relatively cheap here (unless you want a property adjacent to the sea!) compared to Hampshire....indeed my in-laws are moving here from Yateley in Hants.
Good luck with your search!