Hey queequek,
Getting outside of London is normally fairly easy. The trains are pretty good, though people complain about them not being on time. With that said, I've never really had a problem myself. They can get kinda busy during commute hours and they cost a fair bit of money. London to Bristol is about 1hr 45mins and costs about £60 (~US$90) return.
Currently we're having a bit of trouble with the trains. They closed down Paddington Station over Easter for some signal repairs and it took them forever to re-open the station. Since Paddington is one of the main terminals and THE station for travelling out west, that was a real nightmare for everyone. So, if you're taking the train, you'll need to beware of that kind of situation.
The "bus" I hear is a pretty good choice. There is a coach company called National Express (
http://www.nationalexpress.com/) which has loads of coaches going to and from lots of destinations. To give you an example, a coach from London to Bristol will take 2hrs 30mins and cost about £20 (~US$30). I'm pretty sure that you can get them most anywhere in the UK.
I must admit that I'm a travel snob - I always take the train even if it costs more. I simply don't like riding a bus for that long. Either way, you'll get really nice views of the countryside.
Hiring a car is probably not the best idea. Yes, it offers freedom, but it'll be expensive and you may find it difficult to drive on the opposite side of the road (especially in rainy weather). If you're going with a few friends to split the cost, it may be worth it.
Getting to Cornwall is not an easy task. I mean, just look at the map and you'll see why!
Train, bus or car, that'll be one LONG journey from London! If you really want to go there, let me know where in more specific detail and my boyfriend and I might be able to help you put together a game plan.
Also, Stonehenge is a bunch of stones in the middle of a field in the middle of nowhere. Therefore, it's not exactly easy to get to. However, since it's a tourist attraction, there are firms which offer day trips to Stonehenge, Avebury stone circles, Silbury Hill, Wiltshire White horses, Castle Coombe village, and Lacock village. These are normally with 12 people on a mini-bus and shouldn't really cost more than £20, but it depends on the company. Most of them depart from Bath and I think a few leave from Bristol.
Finally, Kew Gardens is fairly easy to get to as it's on the outskirts of London in Richmond. Take the Underground (subway) District Line and get out at Kew Gardens Station.
I believe Richmond is in "Zone 3", so you'll need to be sure to get the correct ticket. Sometimes people get tickets for Zones 1-2 and then didn't realize that they need to get somewhere in zone 3. Simply look at the colour-coded map in the station to check.
Hope this helps!
.....Kelly