We are on the same cruise as you and staying in Newark. we have not done this itinary before but we have been on Explorer of the seas before. It is a lovely ship, food is great, people are great. CH.
One of the cheapest taxis is 'supershuttle' (google it). It's a shared ride in a 10 seater van at a fixed cost. The last time we used it, it was $20 per person & they may or may not have drop off's along the way. You are best to prebook it over the net & on arrival at Newark EWR there are a number of freephones in the taxi/bus lobby & you simply call them with your reference number to let them know you've landed & cleared formalities. As for the cruise it's a great itinerary & very easy to do your own thing at all the ports, with an abundance of taxi/vans eager to get you onboard.........Wilba .
Thanks for your advice much appreciated.