Given you're Gold you'd get free i-net. The hotel's website shows wireless only in the rooms, and there's wireless in the public areas. It also says this for exec level rooms:

High-Speed Internet Access
Guest rooms: Wireless
Lobby and public areas: Wireless
Meeting rooms: Wireless, Wired

Special Benefits
This room features Executive lounge access
Cocktails, for a fee
Complimentary non-alcoholic beverages
Business services, for a fee
Selection of newspapers and magazines
Computers with Internet access and complimentary WIFI access on the executive lounge
Complementary use of Executive Conference room, up to 2 hours (level 5)
Complementary use of Executive Office, up to 2 hours (lobby level)
Complementary parking; private check-in and check-out

It also says this, so sounds like you would be close to tourist things:

Revel in 243 distinct Baku, Azerbaijan hotel rooms and suites set in the heart of downtown.
Amenities include a spacious desk, in-room laptop safe, bathrobe, minibar and iron/ironing board.
Enjoy a restful night with luxurious JW Marriott bedding, custom duvets, and rich, cotton linens.
The latest technology includes flat-screen TVs, Wi-Fi access and iPod/iPad docking systems.
Breathtaking views of the Caspian Sea or Baku city center from our hotel rooms in Baku, Azerbaijan.
Historic attractions, including Baku Boulevard, are steps from your Baku, Azerbaijan hotel suites.

Cheers.