[Lostangel]

True, you would have to sacrifice your happiness to see the houses that are lower than yours. You can always see the houses that are available which are better than your current house. Only certain houses are available in each zone, as Inferno said.
Since your question expressly asked about houses lower than your current house, the only ways for you to get that info is to ask someone who has no house to travel around and send you what is available in each zone, or to do that yourself.