Almost every where is good, but my personal preferences are for:
1) Developing countries, because they are cheaper, there's less traffic and carrying bikes on public transport is often easier.
2) Ex-communist / soviet bloc countries because there's a history of collective land ownership so wild camping is very easy.
3) Muslim countries, e.g. Turkey, Iran and all the 'stans, because they are very hospitable.
4) Big mountains, e.g. the Himalayas, Andes, because that's what it's all about.
5) A reasonable network of secondary roads or cycle paths, so you are not tied to the main roads.
I tend to avoid:
1) Very developed countries, because there's too much traffic and they are expensive, so I'm not in a hurry to tour in the States..
2) Very flat regions (sorry Holland).
3) Countries with high population densities.
Maximum time on the bike, minimum time in a plane or train. Reasonable weather and something interesting to see. This year I am going to Holland and france because the women are 'interesting to see' and the weather is nice, also I can ride all the way there except for the ferry.
You could start close to home to get a feel for the experience. My first few forays into cycle touring was doing Sustrans routes like the C2C - Sea to Sea from Whitehaven to Sunderland or the Dales Cycleway.
The advantages of doing these sort of rides is that many of them have websites dedicated to them:
There's usually links to campsites and B&B cfacilities and a whole infrastructure has sprung up to support cyclists and walkers on the routes.
Have a look at the Sustrans web site for other routes. Some folk aren't too happy with the way that Sustrans routes meander but it has to be remembered that there's no obligation to follow the routes exactly.
To get a taste for what other cycle tourists get up to around the world have a look at:
Chosing a destination is a thing best left to yourself as everyone has their own personal favourite places. Let your fitness, finances and equipment be your guide once you've read up on fellow tourers' accounts.
I think the first thing you've got to consider in choosing a destination (or destinations assuming you are touring as opposed to doing circuits from a fixed base) is your own ability. There is no point in reckoning on 60 miles a day through the Jura (France) if your current experience is popping down to the shops in Lincolnshire.
I would agree with vernon in that you should try something in the UK first but France is a superb place to tour not only for the history, landscape, food and (usually) more predictable weather but also because of the attitude of the French.
Having said all that I met a female cyclist on European Bike Express last summer who was getting off in Orange* (AFAIR) and who blithely said she was going to cycle down to the Danube and then cycle its length. I was quite impressed and asked her how long she'd been cycle touring to which she replied 'Oh this is the first time' !!!
*Just remembered - she got off in Nancy and was heading for Strabourg first
Find out how much time we have to tour.
Pick a place we would like to see.
Turn on the Microsoft auto route express.
Roughly make a route that goes along National parks, ancient ruins, mountains, the sea or ocean and through as many countries as possible.
Do some research on campsites or B&B's along this route.
Finally see if there are trains or planes along the route. We find having shortcuts for various reasons (weather, illness, etc...) makes a lot of sense.
Check out the Touring Tips link on my page.
If you speak/can get by in any language, that's a good start. I'd actually recommend France, Austria, Germany, Holland or Switzerland for a first tour as they're cycle friendly countries and great places to start.
After that, you get the bug and want to cycle everywhere!!
I'd also recommend a company called Exodus if it's your first attempt - we went to India with them in October and had an amazing time. Yes, you pay for their organisation, they're not cheap, but they're good value and we loved every minute. However our next tour will be independent because you just can't beat the freedom!!!
Thanks guys for you advice. I am actually from Australia, so will do some cycling over here.. but I am heading over to England in July and will be there for at least six months so will keep your advice in mind!