Bhutan is a very different kind of a country in South-East Asia. They might be small but they have worked very hard to not let Bhutan become another Nepal. This is why they restrict the number of visitors - which means you will never find a crowd of tourists anywhere in Bhutan. And they ask for a minimum spend per tourist so it is not a cheap destination.
I had travelled by road from Gangtok to Thimphu (approx. 12 hours) and after spending 3 days in Thimphu, i went to Paro where i spent 2 days. I took a flight back to Delhi from Paro.
From Gangtok, i reached the border town of Jaigaon (7 hrs from Gangtok) and spent a night in a small hotel there. Next morning, i crossed the border (in a cycle rickshaw !!!) to get into Phuentsholing where my visa was processed. I further carried on to Thimphu in a local bus.
There are many hotels in Thimphu. Sites like Tripadvisor can help you find some. There are no cheap hotels in Bhutan and you should keep aside a budget of approx. 5000 rs per night for room tariff for a decent hotel. Of course there are very-high-end luxury resorts as well like Aman and Taj where the tariffs can be as high as approx rs. 25000 per night.
You will not find any fast food chains etc. Depending on your travel tastes, you might either find this bothersome or a welcome change. Local food is delicious but typically very spicy. Ema Datshi (chillies in cheese) is the national dish and they eat it everywhere, all the time. Apart from that, 'tibetan' cuisine - momos, thukpas etc are available. A lot of restaurants serve Indian food as well.
According to me, the must dos are :
(i) Visit to the Tiger's Nest (Taktsang temple) in Paro. It is a great trek and a really nice monastery.
(ii) Flight from or to Paro (kathmandu/ calcutta). This route has some great views of Mt. Everest. (See this quora answer here : )
In Thimphu, in their public library, there's a copy of the world's largest printed book. It's a 'coffee-table' book about Bhutan measuring 5 ft x 7 ft. (http://kottke.org/04/10/bhutan-book)
Bhutan is a quiet, peaceful place. Just to stay in the city is also a relaxing experience. You will notice the easy pace of life and the freshness of the air. But you can always take short and long treks around Thimphu and Paro. Some people trek between Paro and Thimphu as well - it is a 7 day trek. Archery is their national sport and it is great fun to see them break into a song and dance when the archer hits a bull's eye.
There's a small night-club scene in Thimphu but why go to Bhutan if clubbing is what you want to do :-)
All cell phone networks work. Not sure about GPRS/3G connectivity. Bhutan is very close to India - geographically, diplomatically and culturally. Bhutanese currency is equivalent to Indian and both currencies are acceptable. However change your Rupees to Ngultrum for a true foreign-land experience. Almost everyone understands Hindi/ English. All Indian TV channels are available and Bhutanese women love Hindi TV serials !!
Enjoy your trip ! Send me a link to your pictures when you return :-)