Before passing a string to eval() I would like to make sure the syntax is correct and allow:
yes, you need the Tokenizer, or something similar, but it's only part of the story. A tokenizer (more commonly called "lexer") can only read and parse elements of an expression, but has no means to detect that something like "foo()+*bar)" is invalid. You need the second part, called parser which would be able to arrange tokens in a kind of a tree (called "AST") or provide an error message when failing to do so. Ironically, once you've got a tree, "eval" is not needed anymore, you can evaluate your expression directly from the tree.
I would recommend you to write a parser by hand because it's a very useful exercise and a lot of fun. Recursive descent parsers are quite easy to program.