Tama Zoological Park is divided into three themed ecological zones: the African, Asiatic and Australian Gardens plus an Insectarium. You can wander around at your own leisure but there is also a twice-daily, 45 minute zoo tour with guides available. A bus tour through the Lion Garden where lions roam free costs 360 yen for adults. The park is quite a distance from central Tokyo so see the link above for detailed travel directions and a full list of animals.
Luckily for cheapos there are three days of the year when admission is free: May 4 (Greenery Day), May 5 (Tama Zoo’s Anniversary Day), and October 1 (Tokyo Citizens’ Day).