I am often required to connect to get things done online. Although there is no longer a need for "internet cafes" since most places have wifi - some of the reliable places I rely on are Seastar Inn, Canoe, Travellers Beach Resort, Alfred's Ocean Palace, Fun Holiday, Charela Inn, Firefly, Sea Splash and Gardenia. Be sure to buy a drink or food if your choice is a place that you are not staying.
You may not be able to access the resort wifi from all their rooms, but it is available and as reliable as you can expect - as long as the attachments are not huge in size. Should that be the case, the fastest internet is at Yellow Computer downtown (you pay for usage) and then probably Gardenia.
Most hotels do have reliable internet connections as they rely on it for their business. They often have a second connection for their guests who tend to do bandwidth intensive things like downloading music/videos, video chats and trying to watch streaming video. This may account for some of the unreliability reports...