Getting to Bristol from London, and day trip to Cardiff?

I am sailing out of Bristol in March 2015 on CMV Azores. I have read there is train service from both Heathrow and Gatwick. I hope to fly into and out of Heathrow with frequent flyer miles. Would be arriving on a Friday morning, and staying in Bristol one night before cruise leaves at 1400 on Saturday. After the cruise, which docks in Bristol on a Thursday midday, I plan to stay 2 nights in Bristol area if a day trip to Cardiff is a good option. Do any of you have any suggestions re: this plan? I have spent a lot of time in Scotland and London area, but not much time in this part of UK. Any suggestions re: transport and accommodations in Bristol will be greatly appreciated.

While in Bristol have you considered taking a look at Brunel's ss Great Britain ship?

http://visitbristol.co.uk/things-to-do/brunels-ss-great-britain-p25861

or a trip out to Bath? 12 minutes by train or 30-40 minutes by road.

There is a National Express coach to take you from Bristol to Heathrow

http://www.nationalexpress.com/coach/Landing/route.aspx?to=Heathrow&from=Bristol&utm_source=google&utm_medium=cpc&utm_term=+bristol%20+to%20+heathrow&utm_campaign=Bristol%20to%20Heathrow&gclid=CJjC8YqylsACFaYewwodLqYAtg

Bristol hotels on Trip Advisor:

http://www.tripadvisor.co.uk/Hotels-g186220-Bristol_England-Hotels.html

Thank you, Ray66. I will look at your suggested options. Have been to Bath [as well as Salisbury and Stonehenge] on previous trips. Thank you!

There are no direct trains from Heathrow or Gatwick to Bristol.

From Gatwick involves a change at Reading.

From Heathrow most folk take the Heathrow Express or the cheaper & only marginally-slower Heathrow Connect to central London's Paddington & switch to the Bristol train, though a shuttlebus from Heathrow to the station at Reading is an option.

Bristol is quite limited, the major tourist draw, as Ray's post, is ss Great Britain. But Bristol is a transport hub for the west-country, so a good base. I guess a hotel in the city centre, or near Temple Meads station, or somewhere between the two. Near the docks is pretty inconvenient, best to accept that will need a taxi or train plus taxi.

Frequent direct trains to Cardiff, journey time 40 minutes, "cheap day return" tickets about £12.

Direct trains also to Weston-Super-Mare (seaside resort, only for good weather), Gloucester (historic dock), delightful Cheltenham, historic Plymouth & a host of other places.

JB :)

Thank you, John Bull!