Posted June 2nd, 2009, 04:19 PM
Sorry for the delay in replying to your query.
Dorset is a rural county with a very relaxed pace of life. There is a marked lack of fast roads and high speed trains but lots of stone built cottages with thatched roofs in beautiful countryside and coastline.
Tourism in Weymouth is mostly aimed at British families interested in seaside holidays in the locality. The combination of these factors means that there is a lack of regular organised visits to such as Salisbury or Stonehenge. A long established local coach operator has the website www.bluebird.co.uk
and the 'day excursions' button gives some ideas on day trips they run, although nothing to Stonehenge.
As you have discovered, Salisbury is not easy to reach by public transport from Weymouth. Ironically, it is only a 30 minute train ride from Southampton if you had docked there.
To visit Stonehenge and Salisbury your best option is to google Weymouth taxi companies and contact them for quotations. Two examples can be found at www.unicorncourtesycars.co.uk
but I've not used either and can't recommend any operator. Stonehenge is approximately 70 miles from Portland. The AA (equivalent to AAA) suggest a driving time of just over 90 minutes, although I think that is very optimistic as you can be delayed by both slow agricultural vehicles and heavy holiday traffic.
As a personal preference I have returned to Salisbury many times but have no desire to return to Stonehenge after one visit. There were too many visitors and you aren't allowed to freely wander amongst the stones but must follow a specific pathway (other than on special tours). I find the pretty village and smaller standing stones and henge at Avebury (15 miles north of Stonehenge) much more interesting and another world heritage site. If you are interested then check out the background at www.nationaltrust.org.uk
and search for Avebury.
If you would like to organise a long do-it-yourself trip using public transport I would suggest a visit to Bath by train. Bath is Georgian city with Roman baths and (slow) trains run there directly from Weymouth. For instance a train departs at 08:50 with a travel time of just over 2 hours and return trains depart from Bath at 15:07 and 17:07. The cost per person is currently 14.70 GBP or about 23.00 USD for a return (round trip) ticket. Obviously you would need to return in good time for departure.
The author Thomas Hardy based his novels of 19th century Wessex around the Dorset county town of Dorchester, about 10 miles inland from Weymouth and easily reached by train (2 an hour, 10-13 minutes) or bus (3 an hour, 40 minutes). All the train and bus times I've given are for weekdays, Sunday times will be different.
You can find out more facts and figures about Weymouth, its weather (we've had blue skies and high 70s for the past week) and surroundings from its Wikipedia entry. It even shows a photograph from Portland across the harbour with Weymouth in the distance.
Sorry I can't be more helpful about getting to Stonehenge but if you want any suggestions for other places to visit with less travelling then please post again.
Whatever you decide, have a lovely trip.