Would like to go to Chester and Liverpool from Manchester.
How are the train connections in this part of the U.K.?
Is public transportation good? Pretty nervous about renting a car.
Would also appreciate any other suggestions for day trips.
Thank you in advance.
I did Liverpool from Manchester as a day trip. Train connection is good.
Both of those are easily visited by train, each less than an hour each way. Not sure how long you're going to be in Manchester but if you want to venture a bit further out (still around 2hrs or less each way) you could get to either Conwy or Caernarfon in Wales or one or more of the villages in the Peak District for some non-city scenery.
You can easily do a train trip from MAN to Conwy - requires one change at Llandudno Junction or take a bus for the final bit to Conwy. (You could then take a bus from Conwy to Llandudno to then catch a train back to MAN). Caernarvon is really too far for a day trip. Note that Conwy is a request stop - so tell the guard that you wish to alight & hold hand out is boarding at this station.
You could also go to York (MAN > YRK) and another day trip could be to Windermere.
www.nationalrail.co.uk will have the times & fares. On some routes, it is cheaper to book ahead - even the day before will give you big savings but at the 'expense' of confining you to specific trains. If you go to Conwy & bus to Llandudno & then train back, you may have to pay for Llandudno to Llandudno Junction as a short hop ticket on the day.
http://www.visitwales.com/explore/north-wales/llandudno-colwyn-bay/must-do-in-conwy
http://www.greatorme.org.uk
http://www.visitchester.com
http://www.visityork.org/?AskRedirect=true
http://www.visitcumbria.com/amb/windermere-lake/
http://www.visitliverpool.com