My first trip a couple of years ago. We stayed in St Brelades Bay which is lovely. It's a very small island in comarison IOW positively huge. Lots to see though, as outlined in what rosie has set out above.
We loved it last year. Be sure to go to the war time hospital in the old tunnels. Fascinating stuff. Also there's an interesting museum in St Helier with an original old house as part of it. We stayed in St Aubin which was lovely and second previous suggestions about the bus service and also the little train. We thoroughly enjoyed the beautiful fresh fish and vegetables in Jersey. Great grub!
Jersey is lovely we have been going for many years. We take our car over but very rarely use it Jersey has an excellent bus service depending on where you are staying. Plenty of lovely walks but we ourselves are not walkers. A nice walk from St Helier to St Aubin with plenty of stop off places. St Elizabeth Castle is well worth a visit as well as the War Tunnels. Good shopping in St Helier with different shops and department stores all pedestrianised. The Little Train from St Helier to St Aubin is also very informative and a pleasant trip. Remember to get rid of any Jersey money you may be given in change you can't spend it in the UK. A guide map is very helpful which you can pick up in various places.