Useless partial answer

Edinburgh- there is a cyber cafe in Bread Street.I don't know what a good cyber cafe is,having never used one, but I've seen it when I passed Bread Street is off Lothian Rd which is off one end of Princes Street- the main shopping street.

There's a new one I saw reviewed a few weeks agao at Toll Cross which is further up Lothian Rd

I haven't been there for a while, but there's a branch of Cyberia in Edinburgh (Hanover Street?) - it was £2.50 for half an hour about a year ago. There's another Cyberia in London - around the corner from Goodge Street tube (Whinfield Street???). I think it's more expensive at around £3 for half an hour. In London there's also a few branches of EasyEverything - I know one's opposite Victoria Station and another one is on Kensington High Street. I've never been to them, but they're supposed to be very cheap. You basically pay for how long you want to use the internet, and food, drinks, etc are also available.

Try a place on Dean Street, just off Oxford Street. It is offering access from just £0.50, about 75c. Otherwise, easyEverything has branches all over the place in London.

In London Debenham's, a department store in the thick of Oxford Street shopping, has an internet cafe that gives you FREE 30 minutes on the internet, after you show your Debenham purchse. No matter how small that purchase is. It's perfect for a few quick emails folks back home, or even some long ones.

Cindy,
It's definitely worth using cybercafes;
"they're a good thing." You have the advantage of relaying how your trip is going as it progresses, can keep up with what's happening with family/friends/work (including emergencies), researching last minute things you might want to do, etc.
As a bonus, maybe you'll make a new friend while hanging out. Cybercafes are easy to use - just pay some money and you are given an account # and password good for a specified # of access hours which are valid until the expiration date, which is usually a couple of weeks or a month. You'll notice that the keyboards used in the UK are slightly different - a few keys in unfamilar locations mainly. There are attendants to help if you have trouble logging on. To check your email you should have an established ISP account that is easy to access from remote locales. I have two ISP's and use my AOL one when going on trips because it's a snap to connect to from anywhere, whereas my other (one I use most) is not. Before leaving on your trip tell people to write to you at that email if they want to get ahold of you (or just say hi) and that you'll check for messages periodically. I was in Edinburgh last month and can suggest a couple of cafes: Cyberia on Hanover Street - go to http://webcam.cybersurf.co.uk and you can see it - and get address and hours.
Their camera is always on and at night after closing is trained out the front window watching the street scene. (You could even tell people at home what time you will put in an appearance in front of the camera and mug a live shot for them). Another cafe was called easyEverything at 58 Rose Street Lane - just west of Hanover (I think). They were just having the grand opening and was quite festive; it was only £1 for 4 hours and is open 24 hours a day. It was just a few blocks from Cyberia and both places are just north of Princes Street. Have fun. Mail lots of regular old postcards, too -- it's always best to ensure that absolutely eveyone else knows what a fun holiday you're having while they work their lives away!