we had wonderful 3 weeks in Myanmar last Xmas.

In short, 2 days is fully enough for Yangoon (people will direct you to main sites and greatest temples/complexes). You can buy good rubies and saphires in local museum of precise stones (obviously do try to do it on teh streets).

3 days is just enough for Bagan (if you like temples and history). You dont need to go there at all if you want to spend your time by the pool (seaside locations are much better for it). The scenery, 100s of temples (I think Bagan covers historical capital of size about 10x20 km, as far as you can see), local people and food are great. We were there 4 days and enjoed every minute (that means we woke up to see every sunrise and stayed out till sunset - cart driver took us everywhere whole day).
Balloon flight is great (we will surely do it next time) if money is no object. I think it is still reasonably prices (similar to the UK level) but it is a real magic to fly over 100s of temples at the brink of sunrise. You should not really compare balloon trip cost to any local costs (we paid 10 US baks to the cart driver for whole day touring the temples, local sites etc).

If you will manage to get to Mandalay - go there and go outside town. The town itself is a damp but there are great historical and ethnical sites in the suburbs. Have a look at the guides for sites/locations - they are about 20-30 minutes form the town centre. You need about 2 days there.

You can fly between main cities. AirBagan and AirMandalay are ok whatever you think from their names, but do not use Myanmar Airways (this is NOT Myanmar International Airways flying to BKK and SIN). It is possible to book flights in advance. Delays do happen so don't plan back-to-back flights (especially when you will need to catch a flight from Maynmar on your last day there).
We also used trains (interesting on short-hop and tiring over-night), river boats, barges, treeshaws (they are still real transport there and not a tourist thing like in Singapore), horse carts, local buses etc etc.

In short, Myamar is a great place to see how much of modern Asia used to be 20-40 years ago (they have no credit cards, no cashmachines and still use American buses left after WWII!), very very kind and friendly people, historical sites, 10000s of large and small temples everywhere (now I realise that Thailand is nothing in this department versus Myanmar).

Sorry I cannot recommend about plush hotels. There are very few of them and we did not go to Myanmar to stay in Hiltons. Ooopps, there are no Hiltons or major hotel chains there at all! Just local establishments (some of them do look well looked after but I think it is very hit and miss when you dont know the place. But I can guarantee that hotel staff will go very long way to make you happy if something is not in order. People friendliness and service was one of my main discoveries in Maynmar.

Hope above summary is useful. Fill free to PM if any specific questions.