Extending range

I have a wireless network on my second floor apartment which I would like to extend into my garage which is on the ground floor and about 100 feet away. The apartment has a large window, but it faces 90 degrees away from the direction of the garage. There is one other small apartment between mine and the outside in the direction toward the garage.

Should I be able to connect to the wireless network in my apartment from my garage? If so, what do I need to do to make this happen? My AP/router is a desktop system running Gentoo Linux. I can buy an antenna if necessary, but I have read that a Wok-Fi can work well.

I also have the task of setting up a hotel with a wireless router so their guests (myself included) can connect to the internet wirelessly. Reception in the lobby would be easy, but could reception be picked up in the rooms 150 meters away with the proper equipment in the lobby?

What inexpensive wireless router should I buy for the hotel that is reliable and doesn't need to be constantly reset?

Does anyone have any advice on extending range? A link or general info of any kind?

I would suggest a more powerful device to start with, most commercial models will totally solve your problem , look at www.zigwire.net
Product Name:AID-2405sg
Product Class:Long Range Wireless LAN system
Features:
* 5 levels of transmit power adjustment ,* Indication of 'connection status,* 5-dbi super rubber antenna, 500mW/27dBm output

This has 5 times the power of what you are using now and will work well. or this outside unit even do a much better job.
Product Name:AMU-2405G-SMA
Product Class:Long Range Wireless LAN system
Features: AMU-2405G-SMA 802.11g/b 500mW , AP/Client/Repeater/Bridge; LED Wan/Lan/Power; Lighting arrestors protection; Stainless Steel adjustable mounting bracket;No internal antenna panel; Plastic outdoor weatherproof case; -30c~65c ,120/240~48vdc power ,up to 30km with Yagi, 16-dbi gain[not included]

Is that the device you would recommend for the hotel? Would it definitely be able to transfer data back and forth with people with cheap consumer grade wifi cards 150 meters away? The hotel is in Brazil so whatever I go down there with I am stuck with.

The AP for the hotel should also have ethernet capabilities. Can the Zigwire do that?

I also need an antenna for the AP in my apartment sending data to the garage. The AP is a computer running Linux so I don't want a standalone AP device there. Can you recommend an antenna? I doesn't need to be an outdoor item.