I am from Utah, but also spend time in Massachusetts during the summer. This past summer, I road tripped from Utah to the east coast, and on that trip I had the chance to do a lot of thinking, and to see a lot of different it areas. Particularly, I thought about how much energy is consumed and pollution produced by traveling cars, the inefficiency of driving or even flying across country, the hassles of dealing with weather, the destruction of open space and beautiful areas in order to make way for housing developments, oil drilling, mining, etc, and of ways to get more vegetation into cites. As I thought about these things and how to make a more generally sustainable society, with more efficient transportation, energy production, and habitation, I realized that the only way to do it on a large scale, either quickly or over a long time. The problem with large scale is it creates large eye sores, are generally a great inconvenience and either cost alot or take a long time.
But what if all of the construction was out of sight? The west is criscrossed with mine tunnels, but people do not notice them, nor do they notice them being made, with the exception of the material coming out. Not only would construction underground avoid bothering anyone above ground, there are also additional benefits. The excavation of dwelling areas could be combined with the mining of natural resources in some cases. Also, underground dwellings would not have to deal in any way with weather or with extremes of temperature. The subterranean lends itself ideally to self replicating habitation because you need fewer materials, and thus fewer tools, in order to make th habitation. If one has digging machines or bots do the excavating, the same bots could also setup a transportation network or any other required infrastructure, as well as performing maintainance as time goes on. There is also the potential for making use of geothermal energy source. Additionally, you can build almost anything you want, of almost any size, because no one has to look at it, and thus they largely do not care. Underground habitation also lends itself well to application on other planets, particularly if surface conditions are extremely harsh.
Of course, some additional problems must be dealt with, such as possible flooding, the lack of natural light, the depth beneath the surface that the construction is done, tectonic movement, the stability of the rock above, what to do with the extracted material. Also, it is generally more expensive to dig a tunnel than it is to dig a trench and later cover it over.
Taking a step back, other habitation possibilities might be living structures, probalby grown from trees and other plants. The benefits of these are that they are above ground, have good insulating properties, are largely self repairing, last a long time, add additional support to the soil around them, cut down carbon dioxide levels, cool the area around them, etc. Downsides include the length of time required to grow a house, potential of allergies, amount of water and other nutrients required. However, these can probably be avoided through hybridization or genetic engineering.
Assuming a world in which there global warming has flooded most of the planet, living underground might not be as much of an option in many areas, however living underwater might be. some of the potential problems to be dealt with are current, ocean life and impact on it, massively redundent water proofing and air provision. Depending on the depth of the habitation, it pressure may also become a major problem. However, it does provide the possibility of homes that are able to relocate. Also, water is a very good insulator, and temperatures at sea vary far less than those on land. Of course, another potential problem is the need to develop a new means of transportation to get from one group of habitats to another.
Another possibility is to make use of aerovehicles, which make use of both bouyancy and aerodynamics to stay aloft, and live in the air. This might be one of the least practical and most difficult solutions to pull off, but it might all work well on a gaseous planet. Depending on the altitude the vehicle is at, it may or may not have to deal with severe weather, but it also might have to deal with extreme cold and lack of oxygen.
Lastly, assuming we find that this planet is no longer habitable, and neither are any others, we could make habitats in space. There are many benefits to this, including the low amount of energy and force required to assemble and move building materials, and the ability to travel through the stars. Some of the main problems are the lack of gravity, lack of air, water, and other vital resources. Currently the cost of getting materials into space is extremely prohibitive, due to our (relatively) dense atmosphere and high gravity. However, it might be possible to mine other planets for resources, and if you build green houses into the habitat/ship/station, and include a method of creating water, it is possible to get most if not all of ones resources cheaply. The biggest problem remains gravity, and the solution to this depends somewhat on the size and design of the habitat, but centripetal force has thus far been a relatively good substitue for real gravity.
In the end though, any solution must be sustainable, durable, and environmentally friendly or beneficial. It must be able to withstand or avoid outside forces, such as weather, impact, or vacuum. Personally, I am willing on designing any kind of habitat, but I am most interested in designing one which might be able to be made in the near future, or at the very least is designed to help avoid the destruction of our planet, and to help people live better. One last possiblity I forgot to mention is the creation of habitation for poor people, refugees, etc. These homes can be designed in very large number of different ways. They might use and make concrete, or they could harvest vegetation to be used directly for building materials or converted in to plastics and then used. They might use a recyclable resin, capable of being melted down and reformed any time it needs to be repaired. Anyways, time for 100 Year Old Physics.
PS: I realize that I have mostly just outlined problems for building any several different environments, rather than suggesting actual designs and solutions, sorry.