I myself have several ways to build zoos, but they all carry one theme. Mainly, large savannah exhibits. Everyone does it. There's nothing wrong with SOME peer pressure.
The savannah exhibits are so popular because A, you get several savannah animals early in the game, and they are very cheap. B, some of the later savannah animals (Black rhino, african elephant) are very popular. C, guests LOVE it when animals are all together. D, a lot of the savannah animals, if not all, are from africa. An exhibit is considered more educational if all the animals in it are from the same geogrpahical region.
So yes, a large savannah exhibit is pretty much always in order. But for actual design?
For a challenge zoo with a moderate/large ammount of money to start, I tend to build a food court right at the front, with two or three exhibits leading off from each side, with plenty of attractions and animals (All my animals are coded to give a full refund when put up for adoption, so I tend to have lots and put an emphasis on my breeding programs). I then make sort of a 'spiderweb' zoo, where there are exhibits that connect with paths, or 'block' zoos, where there are square/rectangle exhibits with a solid strip of pathway inbetween everything.
For challenge zoos starting with little money, I build a few food stands (By few I mean hotdog and soda with a small bathroom), with one exhibit featuring Gazelle (because they breed like rabbits, and remember my refund?), and wait until I get enough money to work my way up.
I try to limit myself to freeform when I want to try stuff out. I avoid using various cheats which I have coded into the items and animals in challenge mode, but in freeform I use them to my advantage. For example, if I want to try a new zoo with only one exhibit for each biome and try to get every animal in the game in my zoo, I'd start with a freeform zoo where I can quickly design my zoo, and adopt all the animals instead of having to wait and earn money (and fame). Then if they all kill each other, no great time or effort is lost, and I can try something else. The 'cheats' I have made include various quirks that items have (say, making all the animals simply LOVE having the Small Fountian in their exhibits, and it will make them all super happy, which I use in freeform when I am trying to see the effects of happy animals against other happy animals, for example), or being able to feed/water your animals in zookeeper mode (a hack downloaded from this site).
So... if anyone is interested in the kind of cheatie coding I do, you can PM me about it. I've been hanging around Zoo Admin for a few months now, even though I made the account somewhat recently. I know how to code most everything, but I don't want to do coding for created animals, sorry. Right now I'm working on a building and scenario, since we seem to have few of those avalible for download.