OTA antenna
Real answer depends upon several factors, terrain, distance to station, station power and receiver used. THEN there is the antenna, the location, and the gain. But unless there is a signal to start with, you are out of luck.
In General, most (90% or so) of the locals broadcasting HD do so in the UHF spectrum. There are some links to see where the stations are located in regards to your location. If they are within 60-100 miles and the terrain is mostly flat, a good UHF antenna with a gain of 12 db or more will probably pull in the stronger stations. Since you have a two story house, you may not want to go on the roof and you can try a UHF antenna in your attic. If the signal strength on the TV shows less than 50%, you will definitely see an improvement with an outside antenna. If the signal strenght is 60% or more, the signal will lock in OK and placing the antenna outside will not be worth the effort (aside from rain, fog, etc)
You can purchase an OTA desk top box at several places for under $200 and try it with a suitable output (components, HDMI, etc) to your set). You can start with a few feet of wire (or rabbit ears) near the TV to see if there is any signal whatsoever there. From there you can postulate as to what you might be able to receive. UHF is mostly line of sight but it will penetrate most walls and roofs but the signal will be attenuated.
Most OTA desk top boxes as well as the Dish 811 use first or second generation HD decoders. The newer dish receivers like the 211 most likely have the latest generation receivers, but you will have to subscribe to a qualifying package to get the OTA part of the receivers to work.