Speakers need to be placed close to back wall. Help

I had the same problem and choose Harbeth's. They have a port in the front, whereas most speakers have ports in the rear of the speakers making the bass muddy when close to a back wall. You can find used (and new) ones easily for your price range nd they have several sizes available. They are good for all types of music, especially voice, although heavy or death metal is not their best forte. They also sound good even with low "Background/dinner music" volumes, which many speakers are poor at. 

Obviously speakers with sealed cabinets would also work or any 'monitor' type speakers front ported. Just mainly avoid those ported in the back in my opinion. Hope this helps.

Any single driver full range speaker (Mark Audio, Omega etc) or full range with a super tweeter (Zu, Devore etc.) work better that close to the wall.

If they are not hifi nuts, they probably would like the sound of any decent speaker placed near a wall. It gives a bass-heavy jukebox sound that non-audiophiles find appealing. The Axiom speakers from Canada will be fine. I set some friends up with a system like that, with the speakers set up against the wall and they think it’s great. .

Many thanks so far, folks!!!  My spirits are lifting.