If you were staying in a city centre, I'd never recommend you to rent a car. However, since you will be out in areas where public transport is not as frequent, you may be better off with a hire car.
Please keep in mind that adjusting to driving on the left can be mentally intensive if you're not used to it. Your urban driving skills will come in handy, but it's staying on top of your natural instincts that is the hard part. Developing a mantra like "driver in the middle" can help remind you what side you should be on when there are no other cars to orient you.
Speaking generally, drivers here are better trained and more polite. When roads are narrow, which is often, drivers will make way for each other so you have to ease off the natural aggressiveness that comes with US urban driving. Take your time and be patient. If someone makes way for you, giving a little wave is polite and appreciated. Have a look at the types of road signs you may encounter so you are prepared:
http://www.direct.gov.uk/en/TravelAndTransport/Highwaycode/Signsandmarkings/index.htmYou MUST hire a satnav or you will get lost. Seriously. Addresses here do not follow the same rules and postcodes will be your best friend in the UK. Also get used to the idea of signs that will tell you the direction you are going based on destination rather than direction. For example, if I am traveling on the M4 from Cardiff to London, the signs will not say M4 East, they will simply say London. This is fine if you know where you are going. But if you have no clue this is another time the satnav will keep you on track.
Are you able to drive a stick (manual)? That would be helpful, although you have to shift with your left hand. (The clutch/gas pedals are in the same config as the US though.)
I've never hired a car in the UK so I have no idea about extra changes, but it's worth looking into in advance to avoid any unpleasant surprises.
I think it's totally doable if you know what you're in for. Good luck!