There's plenty of apps out there to [...] figure out the password.
Well, yeah, those are dictionary attacks. It doesn't matter if you're using AES-256 or FOOBAR-1024, if you choose a weak password it can be broken easily. The only thing that helps slightly against dictionary attacks is using an expensive key derivation function. From a comment on the question below, it appears that 7z uses 2^19 hashing operations to derive the key, probably giving some protection:
Is encrypted 7z/zip safe? How safe is it?
I haven't reviewed their code myself, but I would hope they are as strong as the underlying cryptographic primitives (e.g., 256 bits of security for AES-256). If a tool is so broken that it is not clear from its interface or documentation which cipher is being used at which bit strength, then don't use it.
256 bits of security is plenty safe; in fact, your password will almost certainly have fewer bits of real entropy than 256 unless you are very hard core.
Are there any alternatives for encryption that you don't have to install any new programs to use?
Depending on your definition of "install", you can use a custom LiveCD or virtual machine to run programs without "installing" them.
Which is better to use? 7z or zip?
zip, assuming WinZip AE-1 or AE-2 format is used for actual encryption. It uses standard protocols like PBKDF for key derivation, and others have probably written compatible software, so any discrepancies would've been noticed by now. 7z is just not in the same league.
OTOH, if you're using a random zip tool's "password protect archive" feature that doesn't mention AES-256 or PBKDF, it could be god-knows-what.