Router PlacementForum User - "Well I feel really dumb. After moving the router away from other electronic devices my speeds are back to normal. Just a heads up for anyone experiencing slow speeds, you might want to move it away from other electronics and see if that helps."
3-6' feet minimum safe distance between devices.
Placement on main level floor and central in the building and WELL ventilated is preferred. Not in basements or closets as building materials, or near by electronics devices could interfere or hinder good signal propagation.
Placement in the house is key, central and on the main floor is best for good over all coverage.
Also looking at the User Manual, I just remembered that this model router doesn't have custom QoS features, just works automatically. This may not be good for Xbox gaming. I forgot that some lower end model routers don't have this ability. I believe the DIR-636L does. I'll have a look at the manual, I know the 645 and 655 do. We can help you get XBL set up and working well. I recommend LAN wire connecting the Slim to the router. The new router you get will probably not work well with the Slims on-board WiFi adapter. If you need to keep the Slim on a wireless connection to a router, you can install a DAP model Bridge on the Slim and connect the bridge to the main host router. Something like a DAP-1360, 1522, 1525 or 1533 will work well. I've used the 1533 on my xbox before for gaming on WiFi. Wired is best though.
Let me know about the 815, i'd like to test one out.

And to confirm, the 636L does have custom QoS features.