Books:
Carcopino's
Daily Life in Ancient Rome is a bit dry, but is an old standard.
T.W. Potter's
Roman Italy is good; it has some historical chapters about the development of the Roman Republic, and chapters on things like the countryside, trade, temples and religion, cities and urbanization, etc. It has lots of good pictures.
The Perseus Digital Library is a major site. It has classical texts and translations, photos of sites and artifacts, and some public domain (and so mostly older) reference works. If you want to read some primary texts, this is a good place to go.
http://www.perseus.tufts.edu/
Here's a page on the ever-confusing Roman system of names.
http://www.vroma.org/~bmcmanus/roman_names.html
Lacus Curtius has loads of good stuff. Their "photo albums" of Roman towns and monuments may be especially good for you.
http://penelope.uchicago.edu/Thayer/E/Roman/home.html
The Forum Romanum also collects public domain works. Their online copy of The Private Lives of the Romans may be useful.
http://www.forumromanum.org/index2.html
For sheer squiffy coolness, here's a collection of links to various collections of papyrus (ancient paper). Many of them have educational pages and pictures of stuff in their collections.
http://odyssey.lib.duke.edu/papyrus/texts/homepage.html
Diotima is focused on studying ancient women and gender issues.
http://www.stoa.org/diotima/
Here's a site called the Illustrated Roman Empire, which I haven't used but which looks like it has interesting stuff, including interactive maps. (They're using the term "Roman Empire" pretty loosely to mean "ancient Rome", not just the period that historians call the Empire proper. If you're looking into pre-Christian Rome, you're going to be most interested in stuff through the first few centuries A.D.- it took a while for Christianity to get a real foothold in Italy.)
http://www.roman-empire.net/
In general, I've found Wikipedia's articles on Roman history to be pretty good. This may be your best bet for a place to start, honestly- go click around on what interests you. Here's a list of topics related to ancient Rome.
http://en.wikipedia.org/wiki/List_of_topics_related_to_ancient_Rome
Other stuff:
If you can get ahold of the HBO series
Rome, I highly recommend it. From the few episodes I've seen, they put an immense amount of effort into getting the details right- for an immediate taste of what the city looked like in the late Republic, it's superb. (Though be warned that it's quite graphic in places.) The old BBC(?)
I Claudius is also good.