Destination for honeymoon in early December
 

Me and my gf will be getting married in late November and plan to go on honeymoon from November end to early December. Need suggestions from you guys on the destination.

Here are things we have decided so far:
1. Travel for 10-12 days. Max Budget is to $3000 including hotels but not including flights.
2. Thinking about visiting two locations and spend time in that location and around it. At least one of the location has to be on the coast (Beach is not a big attraction for us but we love ocean!). So for example, we are thinking about Paris + Nice.
3. Weather is not a problem. We are ok with cold place including snow, but it shouldn't be raining every other day for several hours.
4. We want to do at least one adventurous activity. By adventurous, I mean things like bungee jumping, paragliding, skiing etc. We both have never done any of these, but would really like to do something adventurous. Suggestions needed here on what other things we can do as adventure.
5. Apart from adventure, just enjoying time together seeing scenery, some museums, perhaps a play or some show, walking around etc.
6. I am leaning towards somewhere in Europe. :) I know weather will not be great in most of the cities, but then they will be much fewer tourists around .
7. Age: around 27 and if it matters, my gf has never been outside India. And both of us are vegetarians and only languages we know are English and Hindi.

Locations we have thought so far:
- Paris + Nice (though wondering if Nice will be too quiet and dead and couldn't figure out what adventure I can add to the trip).
- Barcelona + ?? (may be somewhere France?)
- Italy or Greece or U.K. (concerned about rains)
- Switzerland (way too cold to enjoy?)
- Australia (concerned that it will be too expensive and 10-12 days is not enough time to explore such a big country)

Look forward to some suggestions!
We thought also to include a short road trip but not sure as we will need to be driving on the other side than we are used to. Surely, I do not want any tickets or potential problems. Any advice/experience on this from people who are used to driving on left side?

It's not Tunisia. You can get two weeks at a 4 star all-inclusive resort for around $1500-2000. They'll speak English and there are numerous vegetarian options at every meal.

"It's not Tunisia." should read "It's not Europe but have you considered Tunisia?"

Addressing the adventure bit: for about $20 you can go on a camel ride or go horseback riding on the beach, for about $250 you can take an overnight excursion into the Shara and also visit the Star Wars sets and Tataouine, plus there are numerous other activities available..

Thanks Sparkchaser. I will look into Tunisia option.
More suggestions needed!