There is a bit of an oddity in your question. Do you mean searching for a mnemonic that starts with certain word(s) like vanitygen does to addresses or actually deriving a single child address that starts with certain characters?
There is no tool for the former and it is not efficient or useful to make one for the later.

What exactly is your goal here? Why not use a simple mnemonic generated by the usual deterministic wallets? You can use that on your "mobile and PC with full access"...