Yes, a good climate would be nice. I also would prefere a tropical paradise if there would be a free choice.

But please consider that we are looking for a territory, which could realistically gain independence by peacefull means and be able to sustain groving population. This means that the area in question shall be large enough and possibly not of an overwhelming importance to the initial power. It is clear that this would be not the best piece of land, because otherwise there would be already a population and economy there. We cannot expect such a territory to be a land of milk and honey, which we could bye for a couple of dollars.
What we need (in my eyes), is a rural territory of considerable size with a potential to develope an urbanity within the next 40-100 years. The area should have sources of water, clay, wood and enough territory suitable for agriculture. The rural character of the area would allow the initial inhabitants to provide at least with food and houses, without being excessively dependent on the help from outside. Yes-yes, the beginning will be humble and more of an agrarian nature, though the future government (or whoever responsible) will have to do a great job while encouraging industry to settle there. The proceeding of urbanization would go hand in hand with increasing population, but the land mass as such must be big enough to enable this developement. What shall we do otherwise, when the initial village of 700 gay nationalists stting on 2.8 km² will grow to a city of 100,000? The area must be larger.
I am not afraid of beginning building up a "national economy" right from the scratch. Most problems of the so-called third world countries result from breaches of traditional society structures, uncontrolled population growth and a generally low level of education. Not every poor country is automatically to be considered as a "third-world-country" in the narrow meaning we usually believe it to be (half-naked starving people without any medical supply). We shall take (one more time) Israel as an example of a state, which is successfully utilising manyfold talents of its citizens and turning a desert into a flourishing land of gardens with healthy economy.
These considerations moved me to inspire the focus of debate be moved avay from tropical islands to different, less paradisic but probably more suitable regions. Of course, Kerguellen was just a provocation to make you think about something different than a coral beaches and long drinks.

Though we have an considerable amount of cooks and restaurant managers among us (Vizier, Feral, Lord Karnickel and even the LP from the GLK!), there are also a lot of people with professions related to the heavy industries as well. If we would be able to arrange a deal with a friendly government about a larger piece of land located somewhere in a moderate-climate area or even a bit colder, we should take it without further hesitation. Remember, our primary goal is political independence in order to enable unrestricted immigration of GLBT people and a safe life in freedom there; a possibly agreeable climate would be of course a highly welcomed bonus, though.
Gaining political independency (beginning with a kind of self-administration, I think) will be a difficult process at any terms, be it an overseas territory of France, a territory in Canada or Brasilia or an islet in Bahamas. The process will be very complicated and to be performed in a legal way which will secure our proprietary rights and the right to reside on the territory which we would bye one day. Just imagine us having spent 15,000,000 EUR for an islet on Bahamas and become imprisoned there for secessive activities with complete confiscation of posessions. Sounds weird but could become a reality pretty quickly. Besides, the neighbourhood is rather hostile against homosexuals there, our defence spending could become extraorbitantly high there.

Of course, we should keep this island on our list (it is not
that bad!).
I would like to encourage the discussion to take into consideration preferably this 3 points:
1)
What do we want to get in the ideal case,
2) What is the
worst still acceptable offer, and
3)
What possibilities do we have
to develope any solution (2) towards (1)?
For example: we could buy a very cheap tropical island of 10 km² but without any infrastructure and no fresh water on it. Shall we sign the deal or not? Solution: We can install a water desalination plant and do pretty well!The larger Mexican island you suggested before is still my favorit. Alternatively we could look for a cheap area in Canada or Brasilia, as well. These nations would surely not bomb us in the case.