How do I set up a wireless network to enable Airplay on an Apple TV when there is no wired internet connection (e.g., in a hotel) using an Airport Express 1st gen 802.11g/n and iPhone 4S?

How do I set up a wireless network to enable Airplay on an Apple TV when there is no wired internet connection (e.g., in a hotel) using an Airport Express 1st gen 802.11g/n and iPhone 4S?

I frequently go to hotels where there is only a wireless connection.

My goal is to enable Airplay so I can mirror my iPhone 4S on the AppleTV and play a game on the phone which mirrors on the TV.

I carry an Airport Express 1st Gen with 802.11g/n. Ideally, I'd also like to incorporate an internet connection, but the only way to get Apple TV enabled is to call up the hotel tech support and register the MAC address. Then, the phone and AppleTV end up on different subnets and it doesn't work.

What I carry:

1 HDMI cable

1 AppleTV 3 and power cable

1 iPhone 4S and charging cable/AC adapter

1 iPhone 4S to HDMI adapter

1 iPhone 4S to comosite cables adapter

1 Windows 7 laptop and power brick

1 3ft. ethernet retractable cable

Any suggestions would help. Maybe manual IP addressing scheme? Will the AE work as a bridge and does that make sense somehow?