Being Catholic, can I attend the prayer meeting of a different denomination?

It depends on the group concerned. If there are no Catholic groups near you, it can be a possibility only if they are truly ecumenical in nature. Which means that they acknowledge that what we have in common is more important than what we disagree about. However, the sad truth is that such groups are rare. Generally, large  prayer meetings are okay but soon they invite you to their Bible study and then things get off track. Such visits can become occasions to deviate from the true faith. So caution. 

Yet if you are firmly rooted in your Catholic faith and are well-informed to answer the questions they generally ask, it is be good to associate with non-catholics. – to pray together, share the richness of your faith and listen to theirs and most especially to pray that Jesus’ desire that ‘there will be One shepherd and one flock’ will become a reality. 

It is also worth noting that The decree on Ecumenism (Vatican Council II) calls upon all Catholics to work for Christian Unity. Yet that can only begin with a true understanding of our faith and history. That is a good place to start. And perhaps we can pray with Benedict xvi ” Lord, remember your promise. Grant that we may be one flock and one shepherd! Do not allow your net to be torn, help us to be servants of unity!” (Pope Benedict xvi)

Also, on a side note, If your area, school or college does not have a Catholic prayer meeting, you are encouraged to take advantage of the opportunity and start one.