How 'bout something which demonstrates respect for the lost. I'm thinking of something that treats them as friends, not as salvation projects. Some of the goofy things Christians do to reach out are embarrassing. Stop it! Oy vey.
Try these ideas on for size.
My wife and I interact with a good 50+ unbelievers on a regular basis - about half of them weekly and the other half monthly. She is a marathoner and trains with a group of women, almost all unsaved. Her best friend is one of these women. She was also playing bunco with another group, but that didn't work so well as half of them lived out of town. This is a really good way to meet people.
I play basketball every Saturday morning with a group of guys - mostly the same 10 - 12, but there are about 10 more who come at different times. I am on a non-Christian, non-church-based coed softball team. We are all very close friends.
My wife and I together also have board games at our house usually monthly of which only one or two of the 10-12 are Christians. This is mostly a different group than my bball friends and the softball friends.
We also play poker with another group, both a public and private game so there are two different groups there, but the private group is our tightest group of friends. We also have potlucks together, do wine-tasting (in house) and sing karaoke. These are not drunkard types by any stretch of the imagination, but are very respectable people. (Of course, I don't suggest you go the poker/wine route if you have major problems with that and I am not interested in a discussion about the theology of it. I have an M.Div. and I can determine what the Scriptures say about it, not to mention I ran the poker bit by 3 colleagues before I started - one a Baptist pastor and the other two independents.)
Some of these folks call my wife and I regularly to hang out. They know we are pastors and are not afraid of us. They call us to help them with various activities - charitable events and the like - because they know we are servants.
What is the key to all of this?? These are our friends. We love them and they love us. We do not look upon them as subjects for our salvation project, but instead we look at them as friends whom we do not want to see become lost for eternity.
We are also members of an online forum where most of the people are not Christians and we have made many other online friends. I switched my doctor to one of them and now he plays basketball with me. Another guy is a major political campaign chairman type of guy where I live - in a large capital city. Both are non-Christians, though they are Republicans, so that is an inroad right there.
Among all of these friends we have had occasion to share God with them in various ways, according to God's timing. They respect us because we respect them.
Scott 8-)