The Astro City is a great cab. If you just want to hook your 360 up to it, there are nice solutions out there such as this:
Just buy an Advanced Scart cable from Microsoft off eBay and connect your padhacks, Paewangs or PS360s to those green screw terminals and you’re done. 31kHz interlaced looks really great actually with this unit, sure it flickers a bit in menus, but during gameplay it’s golden. And it’s basically plug and play.
Get this cool piece of kit from: http://etim.net.au/scart2arcV20 ($115 Australian + shipping)
If you want to run other consoles such as PSX/PS2/Dreamcast, just use the multi-console controller PCB of your choice instead of a padhack or the above mentioned ones. Only the 360 is incapable of outputting 240p arcade resolutions, but most PS2, PSX and Dreamcast games will.