Block ciphers as secure as AES but immune against cache timing attacks?
There are no efficient attacks against AES that I know of (not counting the related key attacks on AES-256). The minimum security offered for AES-128 is still around 126 bits, and that's with pretty inefficient attacks. Furthermore it is studied very well, so nobody is going to present a cipher that has seen so much cryptanalysis (other than its predecessor DES). So yeah, "as secure" is going to present a problem I guess.

If you look at a cipher that doesn't use a Feistel network you might want to have a look at Threefish. It is a tweakable block cipher with a larger block size, a large number of rounds and large key sizes. As it is part of Skein, a SHA-3 finalist, it did receive some cryptanalysis. The main attack against it is a key distinguishing attack, which is not practical for the full round version and is not applicable when Threefish is used solely as a cipher. Oh, yeah, and it doesn't use tables :)