Getting a residence permit 'sans activité lucrative' was no easy process. Understandably, the Swiss do not want people moving here who are then going to be a financial drain on their system. There were a lot of stages to go through, a lot of paperwork, and it was not a very clear process. At one point they went to London to the Swiss Embassy, having been told that this was a place where they could get some vital part of the paperwork signed and stamped, and were told (having got there, waited for ages etc.) that this was not possible. My mum was fluent enough in French to explain their disappointment, frustration and confusion and the member of staff made an exception.
As others have said, buying a property in Switzerland is no easy matter. Non Swiss persons are not permitted to purchase property 'just anywhere'. My parents, when looking to move as close as possible to Lausanne (where our church is), found the closest place they could buy was in a village just above Montreux - no short journey. So perhaps you need to investigate where you will be able to buy property.
And yes, my parents have to pay tax on the potential income that they 'could' get were they to rent their two-bedroomed apartment out, even though it is their only residence.
As others have said, doing your 'sums' is important. I know of another couple who retired here and had to return after 3 years because due to the changing economic climate, exchange rates etc. they were not able to support themselves here.
I would suggest you purchase a copy of Living and Working in Switzerland , which is very helpful, and perhaps the book about buying and renting in Switzerland by the same author. I have't read this one myself... but the first is very helpful.
And if I may make a suggestion based on my personal experience... think about what you will do if it all goes wrong, e.g. ill health, financial difficulties, some other kind of crisis... a back up plan never goes amiss.
The town centre in Geneva is nothing that special, but the old town up the hill is picturesque enough, despite a certain "calvinist austerity" to it. The Carouge district is worth a visit for lots of curious, lovely independent shops and genuine restaurants and cafes, not always full of expats. Eaux-Vives is also up and coming shops and restaurants wise, but apartments only to live there. All around the lake is lovely in the Spring and Summer, but in December, we retreat to fondue restaurants and hot chocolate cafes!
Buying in Geneva is a costly affair, and it's true that 850K will not get you a 3 bedroom-house with garden anywhere in Canton Geneva. Lovely Swiss villages like Choulex, Gy, Jussy, all surrounded by vineyards (wine and food associated to it make the area very special!) are all linked by public transport to the city centre (30-40 mn journey, depending where you need to go) and only 15 mn by car. Hermance or Anieres are right on the lake but you won't get a downright payment out of 800K, on the other hand you would have enough as a deposit for something quite substantial.You can get old Swiss farms split into two semi-detached properties (they still will be called apartments here), then you could get something, just. 5-10 mn farther over the French border (Machilly, Veigy-Foncenex) and your 800k will get you a 4 bedroom architect villa with swimming pool and jacuzzi. A place to keep your eyes on are French villages along the lake: Nernier, Messery, Excenevex, Chens-sur-Leman, all within a range of 25 to 45 minutes from Geneva, with glorious views on the lake and within your price range. But again this might not match your tax requirements.
If you do retire in CH, do bear in mind the compulsory private health insurance, that almost doubles in price for pensioners...expect 1500 CHF monthly!
It's all in the eye of the beholder, and as a wise experienced woman - which you most likely am - I would not let myself be blinded by the exterior of the city (i.e. nice promenade along the lake with views of Mt Blanc, old town with charm etc) but actually take all the negativities you get presented here and use it positively. You probably have a nice painted picture of Geneva in your mind, but each place has it's dark sides, and unfortunately Geneva has it's fair share. Best of luck to you.
On the PPL (Private Pilot License) front. I started taking the PPL (currently hold a VFR SPL) when living in Dublin and thought I'd continue (finish it) here in Switzerland. Was I ever wrong. It will cost 2-3 times as much as in Ireland/UK/US and not worth it tbh. It will be cheaper to fly to the US and get it done in a couple of weeks and return back to Switzerland with a valid PPL. There's also a 4-5 year old thread in here concerning flying schools in Switzerland...
Anyway, the FR flying school link is: http://www.aerodrome-ecuvillens.ch/index.php
Bon chance
To recap previous post, you will hear/read a few negative things about Geneva: increase of crime rate (mainly burglaries and pick pockets), but in perspective, it is nothing like in the U.K., for example. We go to Geneva at night (cinema, theatre, opera, restaurants) and feel totally safe.
Geneva is problably less clean than its sister cities around Switzerland, but again you cannot really complain, it is not bad at all and I still have to trod on a dog poop, something difficult to avoid in some cities like, say Paris (although I do love Paris!).
Some of the ruder behaviour I have witnessed has come from a small minority of expats who believe they are in conquered territory (their bigger offences will be to shout into their mobile phone on public transport or to brag and display how much money they've got, a no-no in calvinist Geneva), but Geneva is big enough to ignore them. Most importantly, and this is why we have decided ourselves to sell our house in the U.K and settle here, if you like the outdoor life, this is all on your doorstep, winter and summer alike. If you like to travel around Europe, then you are right to assume that Geneva is an ideal location (we took a train direct Geneva to Venice, fantastic experience!).
Good luck with your search