There is one notable star cluster in Gemini, Messier 35 [1], which lies at the right foot of Castor (as we see it, it is actually his left foot) above Propus and the faint star 1 Geminorum. About 3,000 light years away, this cluster is 174 million years old. It is the size of the full moon in the sky and fairly bright. To the lower right of Messier 35 is NGC 2158, which is unconnected to M35 as it is no less than 9,000 light years further away. It is not easily seen in a small telescope. It is much more compact (at least as we see it), which led to it being misidentified as a globular cluster until fairly recently. It is an old cluster, being about 2 billion years old. The other interesting object in Gemini is the planetary nebula called the Eskimo Nebula [2]. It lies to the south-west of 5 and below the faint star 63 Geminorum. In a small telescope, it looks like a faint blue-green dot. 

Castor is one of the best-known double stars; the two white stars are bright, but close to each other which makes it difficult to split in a small telescope and needs a high magnification. An easier double star is 20 Geminorum [3], which lies to the north-east of Alhena. The main star is yellow and is faint, and its blue companion is slightly fainter, but they are easily split.