Best way to travel from Heathrow to York? And suggestions on sights from Bath to London?

best would be fly to Manchester then a train direct from Manchester airport to York

alternatively it's the Tube from Heathrow (1hr) then the train from Kings Cross up to York (2 hours)

http://www.nationalrail.co.uk/

Windsor could be a stopping-off place between Bath and London. You could drive there, drop off the car if it's a rental, then take the train to London.

I find lots of things to do in Bath!

-Of course, the Roman Baths are tops, start there first thing.

-I also like the Georgian era so I enjoyed the museum in #1 Royal Crescent, which is a furnished Georgian townhouse. From here you can also get a good look at the Royal Crescent.

-Walk from the center of town up the path marked Gravel Walk to the #1 museum. On the Gravel Walk, duck in to the Georgian Garden if you are either a gardener or a fan of Georgian/Regency/Jane Austen era books.

-You can buy a combo ticket at the Roman Baths that also allows entry in to the Fashion Museum and Assembly Rooms which is interesting.

-The Jane Austen Centre was a waste of time and money in my opinion.

-I did a private walking tour on a Saturday afternoon which was excellent. There is a free Mayor's Walking tour every day that attracts a big crowd.

-Bath Abbey which is right next to the Roman Baths is also excellent. Check to see if there is a concert one of the evenings you are there. Be sure to look at the carvings on the front where you can see angels descending to hell along a ladder. Very interesting.

-Just walking around Bath is interesting, love to look at the weir in the river next to the Parade Gardens with Pulteney Bridge in the background. I've listened to a band concert in the Parade Gardens on a Sunday afternoon. Very nice in pretty weather!

I think this link to the map of the Bath city centre will work.

http://visitbath.co.uk/dbimgs/Bath%20City%20Centre%20Map.pdf

There are also a number of museums I've never had time for, hoping to get to some this next time!

Either Heathrow Express to Paddington, or Tube (Piccadilly Line) to Kings Cross.
Kings Cross to York by kinda 'high speed' service.

Sightseeing options from Bath to London ...
1 Stonehenge - Salisbury Cathedral - Highclere Castle - Windsor
2 Cotswolds - Blenheim Palace - Oxford - Windsor

York has such a strong railroad heritage, I'd highly recommend taking the train, and the scenery is nice along the way!

You could > Land at Heathrow > Railair bus to Reading for train to Bath. Then, train from Bath to York (1 change needed at Bristol) and train back to London.

As mentioned above, heaps of places to see if driving around southern England.
http://www.railair.com
www.nationalrail.co.uk

Note that for these longer distance train journeys, you should pre-book about 10 weeks out for cheapest fares. (For Bath to York, it may work out cheaper to buy 3 tickets = BTH>CNM; CNM > DERBY & DERBY>YRK).

Definitely fly to as close to York as you can. It will save time, money and be easier than transferring to s train after a long flight.

The nearest airport to York with long-distance flights is Manchester. Manchester to York by train takes nearly as long as London to York.

Yes you are doing a triangular journey that might seem to make sense, but if you are spending time in London it would make more sense to do that first - or indeed Bath - rather than York.

Neither Bath nor York has a nearby dedicated airport. You have to travel through Bristol or Leeds. with limited flight opportunities. The UK is so centralised around London that unfortunately it usually remains the best option for arrival/departure.