How can I get to the recycle bin without the desktop icon in windows 7?

Open Explorer (Windows Logo + E) then type "Recycle bin" in the address bar.

That should work just fine, else add Recycle bin to your favorite locations in Exlorer.

Or press the Windows logo and type: explorer.exe ::{645FF040-5081-101B-9F08-00AA002F954E} Which you can of course assign a hot-key to any arbitrary keyboard key or key combination.

Make sure you've spelled it correctly. I just click "Start" > "Computer", and typed rec... then Recycle Bin was shown underneath

I can also type "Recycle Bin" as a whole and it goes straight there.

Sure, just type this into the search box:

shell:RecycleBinFolder