Of course there are things we can do for faith purpose which people can see doing but it depend on the intention that you do it with.
If you did righteousness for show, it has no reward from your father in heaven.
The fear of God is obedience to the Law of God and obedience is the Love of God. Obedience to the Law of God is synonymous to fear of God.
You can say you worship God when the elements of faith is present in you, you cannot worship God without faith. how can you hear God if you don't believe there is God? Without faith you can't please God. What is greater than faith is love, even the Bible say do everything you do in Love.
The only reward is for those that worship God diligently, so you won't be able to enter the kingdom of God if you you didn't have faith again.
We do some things that can't be hidden for people to see and that's not a show off but that kind of things we do still depends on the mind we do it, maybe for people to see or we do it for God, if you do it for show off, then it didn't have reward, you already have it in your mind that it's for people to see it, that's not for God anymore, God would reward only the work you do for him, not the one you do for people to see and God would see it by Himself throught your mind because He sees man through man's mind, not physical that man see. Example of the good work we do that is obvious for people to see is preaching the gospel of the Lord Jesus Christ, you can't do that one in a secret, people would definitely see you and that is the best work ever and like a must for all mankind because we need to try as much as possible for other people to know how good it is to be a Christian because only Christian and this that didn't even know Christ but choose to do the good work would be saved.
Even doing the good work we do our actions, how we behave to people is a preaching on its own, people can watch us and want to join our religion or want to do just like us. But the righteousness that we have to do shouldn't be for show, the shown ones doesn't have reward from God.
When you fear God, it's the same thing that you obey God, it's synonyms. Do what God commanded man to do and don't do things that God commanded Man not to do is what we call obedience to God. Whoever have this attitude or behavior would be rewarded by God right from here in this world and in heaven because when you obey God, you would do the good works, what he Command us to do is the good works.
Without faith, you can't do the good work because it can't be possible for man to do believe or follow someone that they didn't believe he exists. Man need faith to believe that there is God, then man can now do the Commandments of God, without faith, all that man do is in vain, faith need to be the first thing man need, then any other things. The only thing that is greater than faith is Love.
God have reward for man but only to the ones that worship God diligently, reward goes to those that worship God without adding something else with it; like worshipping idols and still worship God.