If you live in a larger city, you could try a new thing called 'speed dating'.....but this is just to see if the 2 parties are interested. Its not for a date that evening. All the prospects meet at a bar or restaurant and each person spends 10 mins with a person, then moves on to the next person and so on. At the end everyone writes down who they liked.

If you're looking for just one event, then you could do what Michael said - there are some who are just a companion and not including sex. I saw something funny on a morning show - it was discussing how people can rent out their stuff - literally anything like a hammer, bike, skis, their car and even themselves but as a 'rent a friend' lol. This one lady rents herself as a friend and that day, she agreed to go on an innocent picnic with a person. Some days she shows new people around town.