I have two outbuildings about 175 feet to the north and to the south of my house. I have internet access and want to get that

I would lay underground quality Ethernet cable and connect an inexpensive router set up as an access point in each building. A totally wireless solution is possible but would be more expensive, such as directional outdoor access points like THESE.
 
I cannot underground cable. Would a Asus RT68U at each location be configured to talk to the middle router? Or, would some external antenna at the middle location be needed? Thank you RealBeast!
 
For a good and reliable connection I would use the point to point outdoor APs that I linked for about $60 each, you would need 4 and direct line of sight.

What is the construction material of the outbuildings?
 


Not sure what you are recommending then. You yourself recommended ubiquiti and point to point links. If have actually used the ubiquiti products you know that you can adjust the power. Although the airgird line is physically large that gives it the advantage of have a much narrow beam width which actually reduces interference between multiple connections. Unless you are designing point to multipoint you want the radio beam as narrow as possible.
 
Yes I have used a multitude of Ubiquiti products including PtoP and PtoMultiP, Personally I would go with the NanoStation line and the locoM2. Point to multi is no good if one barn is north and one south of the base station. I think I'm right in saying the beam is 35° but I would need to dig a few out. Apart from anything else they're not as pig ugly on the side of structure. I've had issues with the higher power NSM365 where you simply couldn't turn down the power enough for a reliable connection over 30m, ended up relocating one of the units as far away as possible and turning the radio down as far as possible.
 
I have internet at house and want internet wirelessly to north building and south building. Want north and south building to have wifi access to laptop, cell phone, tablets, etc. I've read that client mode/bridge mode only allows wired connections and WDS has through-put penalty. Is that right? Was hoping north and south modems could connect to house modem.
 
WDS is just a trick they use to pass multiple mac address over a encrypted wifi connection it has almost no effect on the throughput. What you are thinking of is a repeater and the cheap ones with only a single radio do cut your speed by half. Because of the issues of getting signals though the walls the optimum design is to use point to point outdoor devices. You would then connect them to a AP/router inside the building via ethernet. This is a form of repeater but because you have 2 completely separate devices you do not pay the penalty that a single radio repeater does.

There are repeaters that are designed for outdoor use and the attempt to repeat the signal though the walls but you never really know how well that will work. These tend to be a little expensive when they do it with 2 radios rather than 1.

There are some other designs where you could use a omni directional radio in the central location rather than a point to points. The solution with 2 point to point radio connections and a AP in each building is going to give you excellent performance. I would only look at other solutions if the money is going to be a problem.
 
Thanks Bill001g! So, If I have a dual band router in the south building with an outdoor directional dual band antenna connected to a LAN port and pointed in the direction of the house - a same model router in the house connected to a modem at the WAN port and an outdoor multi directional antenna connected to a LAN port - and finally, the same setup as the south building in the north building. Would both wireless and wired connections be available at all three locations? How would each router be configured? Thanks for all the posts.
 
The key thing that makes it all connect is you are using the LAN ports in the remote building. Internally the lan ports are just a switch. The wireless chips are logically hooked to the switch part of the router so it is all connected. Since there is no traffic going wan-lan the router part of the device is not used. This is pretty much the difference between a AP and a ROUTER

Make sure you disable the DHCP and do not have conflicting ip on the LAN int the remote routers.

Now your routers may have a AP feature but all that really does is make the wan port into sorta of a fake lan port but the traffic must still pass the router process unlike the lan ports that only talk to the internal switch chip. Up to you both method should work well for you.