Well, solutions written in anything non-Lisp-y is going to look very different - and there may well be parts of SICP that rely on features in Lisps, such as macros. Of course there may also be parts of SICP that rely on mutable data which would have to look rather different in Clojure too...
If you don't plan on using Scheme or Clojure, I guess my question would be: Why not?
SICP is written around a dynamically typed Lisp dialect. Clojure is the closest modern equivalent. Other options might be Erlang, F#, Haskell, or Ocaml - although you might argue Erlang, Haskell and Ocaml are not really "modern" so that's why I'd want to know more about your reasoning before trying to suggest other languages...
+1 for Clojure as it would seem to offer you the benefits of a "modern" functional language, plus access to the JVM platform, and as a Lisp language should not offer too many obstructions/diversions in implementing the ideas from SICP.
You could look at Racket which is based on Scheme and is fun to use, although unlike Clojure it doesn't seem to be used much outside academia.
If you're determined to stay away from Lisps, maybe Scala would count as a "modern" FP language which is gaining traction in industry, but you may find you have to spend a lot more time trying to translate Scheme-based examples into an OO/FP hybrid language like Scala with its sophisticated (and fairly perplexing) static type system.
Haskell or ML would spare you the OO diversions of Scala, but you're still dealing with static typing again.