The station area isn't particularly bad, just a bit full of people going back and forth at night. The main station of the tram network is a stone's throw from the Doubletree so that sets up your transport quite well. Frankly the biggest personal safety hazard in Amsterdam is the damned scooters, especially on the cycle paths.

There is a Belgian beer bar called Delirium a short walk along the riverfront east from the Doubletree, it's opposite the Bimhuis (next to the Mövenpick), check the ABV before you quaff

However the biggest collection of restaurants nearby is on Zeedijk with a cluster of Asian restaurants and then a little further on off the end of Zeedijk is the Nieuwmarkt area with the Chinatown of Amsterdam. Or head slightly west into the red light district; it's quite safe from a personal point of view but you run a slightly higher risk of being pickpocketed here than elsewhere in Amsterdam so watch your pockets and bags. You can look at the prostitutes in the red-lit windows but do not try to photograph them.

Going yet further on in that direction you get to the Rembrandtplein (Rembrandt Square), recognisable from the station of Rembrandt looming over the (usually present, occasionally moved for special events) bronze statues of the Night Watch. This has a good supply of cafes, bars, restaurants, coffeeshops, etc. On the way you may have passed Cafe Basjoe, allegedly the oldest coffeeshop in Amsterdam, if that's your thing (beware of smoking the strong stuff and being too wrecked to function the next day). My personal favourite in that area is Zushi, conveyor-sushi but very high quality. I don't recommend the sushi at Shabu-Shabu (and what fool called a sushi bar shabu-shabu?) because it had a low hygiene rating last time it was inspected. Both the Gaucho's and the Nachtwacht steak houses are ok. Coco's is very generic, don't bother. Decent breakfast can be had at the line of cafes on the north side of the square, if the Doubletree fails you. For beer in that area, try Cafe Gollem with its vast selection of Belgian and other beers.

From the station front, you can take tram 9 or 4 to and from the Rembrandtplein if you don't want to walk (I wouldn't blame you), usually from stop 3 on the east (Doubletree) side of the central station. Check out the 24hour, 48hour, etc, tram passes if you intend to take several trips about the tram system.