To me, I think one of the biggest indications that one has a monastic vocation is a love of the Liturgy of the Hours (aka:Divine Office, Prayer of the Church, and Breviary). If I had been more "on the ball" I think I would have realised my monastic vocation much earlier in life. I think that the Liturgy of the Hours is a wonderful way to worship our Lord. As the Psalms open up to you, you can see them on so many different levels. You may see it as King David crying out to the Lord in time of need; you may see yourself crying out to the Lord in time of need; or you may see Jesus talking to you; the same Psalm may hit you a different way. And all of these are valid ways of viewing the Psalm.
I actually did not know about the Liturgy of the Hours before I went to seminary at Oscott College. It was there that I discovered it, and there that I began to treasure this way of praying. If you are unfamiliar with the Liturgy of the Hours you might want to check to see if there is a monastery, religious community, or even parish that prays it near by. The Liturgy of the Hours can appear in numerous forms. If you do not like it at one place check another. Some communities have it in Latin - if you do not understand Latin you may not like it or you might still appreciate the beauty. The American translation is a bit dry in my opinion. I have seen "politically correct" breviaries - one can take that as they will. Also the Roman Breviary take the 150 Psalms over a 4-week period, some communities take the Psalms over two week and some in just one week.
What ever your vocation is, this way of prayer is open to all Christians: married, single, younger, older, priest, lay-person - Everyone. But if you are looking to celebrate the complete Liturgy of the Hours everyday, you may just be called to a monastery.