Hi LilyoftheValley,
I moved to Switzerland last year and currently live in Lausanne, so hopefully I can help you on a couple of points regarding life in this city:
Public transport:
Lausanne has great public transport internally, with bus lines and the m2 metro system providing an effective way of getting around the city. There is also the m1 train the goes from Lausanne Flon out to the western edges of the city region, and the main overland train lines the head west (to Morges, Nyon and Geneva), north (to Yverdon, Neuchatel, Bern, Basel, etc - sometimes including a change of trains where necessary) and east (to Montreux, Villeneuve). As a Swiss resident you can also occassionally (think the limit is max. 3 per person per month) obtain a "carte journaliere", a ticket that allows you to use all the buses, trams and trains in Switzerland for a whole day, as well as certain boat and cablecar services. This is great for days out to visit this beautiful country, and only costs 40 CHF per ticket.
1 - 4 - Unfortunately I don't know a lot on this topic; Lausanne has the CHUV as it's main hospital, a very reputable hospital that is (according to my wife) famous internationally.
5- Good beauty Spa/Clinic, that is somewhat affordable and reputable.
- the nearby towns have some nice spas, such as Lavey-les-Bains and Yverdon-les-Bains; Yverdon is reachable by train from Lausanne (roughly 15-20 minutes), although I'm not sure about Lavey as I have only ever been there by car.
6- Near by access to a place to jog/run, safely
- there are plenty of excellent places to jog that are both public, safe and enjoyable. A good starting place is to go for a jog along the lakeside in Ouchy, where a jogging course is already laid out (this is my preference as it is flat and therefore not too many uphill runs!). There is also the jogging track in the woods at Chalet Gobet, a very popular course. Similarly there is another jogging track through the woods next to Bussigny, but this is more challenging due to some steep inclines in some areas.
7- Nightlife is NOT important. For that we can always take a train somewhere else whenever we feel like it. We are not drinkers, so bars, etc. are not important either.
- Lausanne does have several good places to drink in the evenings, plus a few clubs as well (if you feel in the mood!). I'm not someone who really goes clubbing much, as I prefer to have a drink in a pub where I can actually hear what people are saying; my favourite place to enjoy a drink is the Brasseurs in Lausanne centre (next to the Flon), as they usually have seasonal specialty beers to try and serve some excellent flammenkuche!

8- Be able to eventually find and buy a detached house, with at least 3 bedrooms, a garage and a small garden or enclosed area to have plants and let the kitties out safely. (Somewhat affordable. By that, I mean nothing luxurious, but comfortable and clean) Is this possible below the millions of CHF? Or should I forget all about a house?
- Due to the fact that a large amount of Switzerland's surface is taken up with mountains and lakes, detached houses are something of a commodity; the vast majority of people live in apartments (like myself). The areas where detached houses do exist tend to be considered as prime pieces of land, such as those with a view of the lake/mountains/both, and therefore prices are fairly high. If you want a 3 bedroom detached house with a garden and in a reasonably nice area, the price would be edging close to the million range, although if a nice view is not one of your priorities you can get a house starting from around 500'000.
9- Have sunny days, not all foggy and rainy. I know it rains in some areas more than others. Others don't get much sun.
- I live in the Vaud region and can honestly say the weather is fantastic here. The geographic location of the region - surrounded by mountains - means it benefits from an almost mediterranean climate, and that means summer is very warm indeed. As an example of this, the first two weeks of July this year had temperatures of over 30 degrees every day, with no rain. Also, in September of last year there was only one day of rain (the 4th September - our wedding day!) so it really is a region that has excellent weather. Of course, winters here are cold - the coldest I saw in Lausanne was -12 degrees, so it helps to have a big coat!

10- Have access to stores that are opened past 6 PM - 18,00 hs(We would be at work most of the day, and by the time we get back, if everything is closed, it will make things more difficult) If not possible, we'll have to adjust our routine.
- That might not be very easy to find; coming from England, where most supermarkets are open either 24 hours a day or at least until 10pm, I found the fact that Swiss shops close in the early evening to be quite a shock (limiting my ability to pop out and get food after work). Some shops do open slightly later - our local Migros (a large Swiss supermarket chain) is open until 7pm on weekdays, but the majority will close around 6pm. Oh, and almost all shops are closed on Sundays, so you will have to shop on Saturday otherwise you'll go hungry on Sundays!
11- Prefer NOT to have a long commute to work. 20 minutes approximately, would be ideal.
- That all depends on where you work - if you do work in Geneva or Meyrin, Lausanne has regular trains to Geneva that leave every 20 minutes or so, taking roughly 30-40 minutes. The time spent on the train does pass pretty quickly, although it does go over the 20 minutes maximum you would prefer for your commute. Both Morges and Nyon are closer on the train line to Geneva, so would obviously take less time for your commute (I guess roughly 5 minutes less for Morges and around 10-15 minutes less for Nyon).Other large cities are a bit further away, for example Bern is roughly 1 hour by train and Basel 2 hours. Public transport in Switzerland is excellent, and I have not yet seen a delayed train whilst travelling from Lausanne to Geneva, so at least you would not have much risk of getting stuck at the station waiting for your train to turn up!
12- Have internet access at home (I guess that is common everywhere)
- Yep, the Swiss are as developed as most other countries in that respect. There are also several suppliers to choose from, depending on the region you live in; we went with Swisscom as they offered a package that included Internet and a digital television box (giving us a multitude of channels, including some English channels such as BBC).
Hopefully my answers above have helped a little bit - I am biased towards Lausanne as it is where I live, but I know that Morges is a very nice place to visit so presumably is a nice place to live. My wife's cousin lives in Nyon and I have heard that the cost of living (including apartment rental costs) is higher there than in Lausanne, but that might all depend on where you live - obviously an apartment with a nice view of the lake and mountains will be more expensive than one with a view of the street or another building!
If you do end up living in Switzerland, you will have made a very good choice!

All the best,
Paul