What does the Bible say about praying in public? Should our prayers be in private, according to Matthew 6:5-8?

It seems to me that praying in private is best, but there are some exceptions when public prayer is right. We are not supposed to pray to show off or witness I don't think. Some people think they are witnessing by praying in restaurants, but I don't know whether that is really witnessing effectively. Some people are offended and this is the reason for not praying in public. We can offend some people and we are supposed to only be talking to God and not getting into unnecessary warfare by praying in front of those who might oppose it. Prayer is warfare to some extent (more or less) anyway, so why make it worse?