Depends on the bug you are chucking and the type of water you are fishing, most will need some shot to keep them down.
The main exception will be big stone nymphs, the good ones are all tied heavy enough to fish without shot.
Have a look at the "bedlars double beaded stone" nymph in the top right hand corner of the link. This bug is weighted just right and is deadly for big trout on any river I have ever had the pleasure of soaking it in (they should ban it instead of bait). On of the deadliest flies I have ever fished. They are almost impossible to find so if you ever see them buy them all!
All smaller bugs wil require some added weight except for in the slowest, shallowest water.
As for rivers to fish close to here, there have been lots of recent reports all over the net about the two main trout rivers that we have close to us, try either of them and you will have lots of fun and get some great practice.
Good luck and feel free to PM me with any questions.
PS: if anyone sees that bug let me know!