Agree - the Doubletree is a good option if you want to stay at a Hilton property. It's walking distance from Centraal Station (turn left as you exit, you can't miss it) and in the newly-redeveloped Oosterdok area, which has a number of interesting places to eat and drink. You can walk to the centre quite easily - head down Zeedijk to Nieuwmarkt if you want to avoid the hordes going down the Damrak (or follow the cycle route along the station front and under the main road to the Singel, just by Browersgracht, for fast access to the canal belt and the Jordaan).

The Hilton proper is in an upmarket residential area, which has its own benefits. There are interesting local centres nearby (around Johannes Verhulststraat and Beethovenstraat). From there, you could use the South Station (Amsterdam Zuid/WTC) which also has direct trains to Schiphol (6 mins) and The Hague (36 mins) which saves you time vs the journey from Centraal. It's about a 20-minute walk, or a short bike/tram ride - it's equally a short tram ride from the Hilton to the canal belt, via De Pijp, Museumplein and Leidseplein.

All things considered, I'd choose the Doubletree for a short stay, but I did enjoy staying in the near suburbs on longer and more regular stays (actually not at the Hilton).

The area around Centraal Station is a lot busier and less seedy than it used to be. Do watch your stuff, of course - particularly on the trains between the airport and the city - but I wouldn't be unduly worried.