It's supposed to be one of the most stressful things you can do, but at least as someone with an interest in local history, moving house gives you a new avenue of research.
I regularly speak to people who are checking up on a potential new purchase (chalk workings around the Norwich area are a particular favourite) and might soon be back in this position myself.
When you buy a new property, you get environmental searches done, which generally point out any possible contaminated land, flood risk, radon levels etc. What these don't necessarily tell you is the historical detail; but there are ways for you to make your own investigations to find out more about the history of your plot...
Take for instance a site nearby identified as an old industrial working. The search report might not tell you what it was beyond a general description, nor when it was operating, who operated it or for how long. A visit to a local studies library or record office to view various editions of local OS maps and trade directories would be a great start to get a more accurate description to add to an overall history of your home and the land that it sits on.
As for flooding, you may find the following page useful, which currently has Surface Water Management Plans for Norwich, Great Yarmouth and King's Lynn: http://www.norfolk.gov.uk/Environment/Flood_and_water_management/Surface_Water_Management_Plans/index.htm as well as links to other pages. For historical flooding events you know of, you may wish to consult minutes of various organisations as well as old newspapers.
If you're interested in street names, if no one locally can provide you with an 'answer' as to why a street is called by a particular name, then go looking for published sources. In Norfolk for instance, we have a whole index of mini descriptions of streets as well as several printed volumes, although it must be said these are particularly comprehensive for Norwich, and inside the city walls. Planning Committee minutes may also be worth a try and detective work of your own can also be fruitful. For example, on investigating Trory Street I searched the NRO catalogue to find a particularly influential Trory in that area, who it appears, owned the land before it was developed. Mayors, politicians, reformers and otherwise well known individuals are also often commemorated in this way, so Le Strange's Lists may be a handy text for inspiration.
You might also like to find out roughly when your home was built as this will come in useful, particularly when you come to apply for home insurance. There are many records which may be useful for this, not least the deeds if you have sight of them, and the source that gets you closest to the build date will vary a little depending on the approximate age of your home. Maps are an obvious place to start, particularly if your home has been built since the first edition OS maps of the 1880s. Before this date you still usually have access to tithe/enclosure maps and in Norfolk Faden and Bryant will also be useful as earlier reference points.
You may also find the census useful, if your house was built before 1911 and was described well enough to identify the right building - you will usually find you need to cross reference with other sources. In the city, trade directories may show lists of residents on the street, or when the street appears. Also in the city, you may find a reference in the City Engineers building control plans which arrived following the Public Health Act of 1875 (try NROCAT using 'N/EN' in the CatRef field and the name of your street etc. You'll also find land tax (c1782 onwards), electoral records (1832 onwards) and poll books/hearth tax handy. Visit your local record office or local studies library for more details.
Even if your house is a new build, you'll find that often the land it sits on has a tale to tell. For my current home, I ended up researching the farm the land once belonged to instead!