In order to benefit from the "extended range" offered by a replacement 802.11N "router," you would also need to fit 801.11N wifi adapters to all your client devices too. (Equals extra cost.)
Another contributor here often cites that it's best to think of 802.11N as "deliving better throughput at any given range than ABG" rather than a dramatic increase in the wifi footprint. The "strength" of wifi signals are mandated by law, and N is not permitted to be any more powerful than ABG.
One of the "challenges" with "up the garden" is that you're utilising wifi signals that have transitted from indoors, through the walls and out (and vice versa) thus it's "weaker" but usable signal than if you sat next to the router indoors. However, in the garden, it's more likely that you will also be encountering all the weak-but-usable signals from everyone else in the neighbourhood that has wifi (and that's becoming lots these days.) If you want to check, download InSSIDer onto a laptop, take a wander up the garden and see what you can see. (A few years ago I did this on the corner of Baker St & Marylebone Road in London and found 200 in a matter of seconds - though I did feel a dick sat on the pavement with a laptop.)
To extend the range "up the garden," the best way would be to place an "access point" (no need for a full fat "router") there and cable it back to your main "router." Or maybe experiment with moving your current "router" near to a window that overlooks the garden and see if it's any better.
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