The Hilton is great for location. I stay there almost every time I go to Romania (I stayed at the Radisson Blu across the street last time). YOu can take a taxi from, the airport for maybe 30 RON ($7-8) or the Hilton shuttle if you schedule it is only 40 RON. There is a bus stand right outside of arrivals to the right. 1 ticket is like 8 RON and gets you to Piata Romana then you have a 6 minute walk to the hotel. I've done every one of those things with no problems.
The hotel itself is in the shopping street section of Calea Victoriei and about 1 KM from the main old town part of the city. You will pass the art museum and the Athenee Palace on your way to town. From old town you can cross the river and get to the giant parliament building if you so desire, or you can walk around the city. It is quite friendly with a few museums to see, places to eat, and people watching.
Uber exists there, I have not used it. The taxis have all been fair, easy to find and affordable. The breakfast at the Hilton was nice. I have always been upgraded as a gold even when, as you noted, you book the more expensive room because the standard points are more than the points based on cost prices. A couple of years ago I was upgrade to a 2 bedroom, 2 bathroom suite that I had no need of as a solo traveler
As for the airport in the morning, OTP is a bit of a cluster but it clears surprisingly quickly to me. It looks disorganized, but I have always made it through in plenty of time. If you get a cab or Uber from the hotel at 6, you will be there by 6:30 and get to your gate with time to spare.
For your reference, I have been to Romania 4 times (5th in December this year) since 2013. So that is a little more recent than the 2008 review, but most of the points are still valid in SanDiego1K's post. Check the rates on the doors of the cabs and you will be fine.
