The Xilinx tools can't interface in real-time as far as I know, neither can ModelSim (used by Actel's Libero IDE)
I don't know about open source simulators, there are some rather exotic projects out there so it's possible there is something that could do this.
However, this may be you an answer you didn't ask for (I'll delete it if it's not helpful), but I would consider building your own FPGA board to do this or at least get started along the way towards it. I etched my first FPGA board and though it was very simple (the board not the process ;-) ), it taught me an awful lot quite quickly.
- Jump right in at the deep end and learn all you need to know about the hardware considerations. Forces you to read most of the datasheets first, and write your own starter code, which IMHO is often better than the plug and play dev board approach to learning.
- Only put on the board what you need to.
- Get's you further towards your goal of a real working design with possibly the same effort/research as the figuring out how to simulate it all in real-time would.
- Still need to buy a programmer, although cheap versions of the Xilinx/Altera programmers can be found on eBay.
- If PCB/signal integrity design and issues are not something you wish to focus on, then you may not be interested in much of the knowledge to be gained by doing it this way.
I understand the etching your own board is probably unnecessary, I only did it because I had the FPGAs there, was impatient and didn't want to wait 2 weeks for a PCB to arrive. There are extremely cheap deals out here for 2-layer boards, which would do to at least run your design (possibly at lower speeds than eventually desired - normally the minimum layer count for a high-speed FPGA design would be 4, but these are much more expensive)
Anyway, Spirit Circuits does a completely free 2-layer "bare bones" PCB deal (one a month, one design, no mask or silkscreen) which comes in handy for a one off design.
Also, for proper 2 and 4 layer cheap prototype boards, ITead and Seed Studio go as low as $10 for 10 boards (or possibly 5 at that price) services.