Since I've done a few of these, maybe I can be of help. I've been to most of the ports, and heading west is the way to go. This world tour would begin and end in NYC...seems fitting, since it's the center of the universe ;)
1 - NYC
2 - St. Georges, Bermuda
3 - Charleston, South Carolina
4 - Miami
5 - Bahamas
6 - St. Maarten
7 - BVI
8 - Puerto Rico
9 - La Romana, Dominican Republic
10 - Port Antonio, Jamaica
11 - Havana, Cuba (oh sorry, Americans can't go there)
12 - Grand Cayman
13 - Cozumel
14 - Roatan, Honduras
15 - Curacao
16 - Bridgetown, Barbados
17 - Rio De Janeiro, Brazil
18 - Buenos Aires, Argentina
19 - Falkland Islands
20 - Antarctica
21 - Valparaiso Chile
22 - Santiago Chile
23 - Galapagos Islands
24 - Easter Island
25 - French Polynesia
26 - Cook Islands
27 - Hawaii
28 - Costa Rica
29 - Acapulco
30 - Cabo San Lucas
31 - San Diego
32 - Catalina Island
33 - San Francisco
34 - Astoria
35 - Victoria
36 - Seattle
37 - Vancouver
38 - Parksville
39 - Queen Charlotte Islands
40 - Ketchikan
41 - Juneau
42 - Skagway
43 - Glacier Bay
44 - Anchorage
45 - Adak, Alaska
46 - Petropavlosk, Russia
47 - Vladivosktok, Russia
48 - Otaru, Japan
49 - Hakodate, Japan
50 - Tokyo
51 - Shimizu
52 - Kobe / Osaka
53 - Hiroshima
54 - Nagasaki
55 - Naha (Okinawa)
56 - Cheju, S.Korea
57 - Pusan, S. Korea
58 - Mokpo, S. Korea
59 - Dalian, China
60 - Tianjin (Beijing)
61 - Qingdao, China
62 - Nanjing
63 - Shanghai
64 - Putuoshan, China
65 - Ningbo, China
66 - Xiamen, China
67 - Taipei, Taiwan
68 - Hong Kong
69 - Macau
70 - Manila, Philippines
71 - Cebu, Philippines
72 - Boracay, Philippines
73 - Da Nang, Vietnam
74 - Ho Chi Minh City, Vietnam
75 - Pattaya (Bangkok)
76 - Ko Samui, Thailand
77 - Singapore
78 - Bali, Indonesia
79 - Darwin, Australia
80 - Cairns, Australia
81 - Whitsunday Islands, Australia
82 - Sydney
83 - Melbourne
84 - Hobart, Tasmania
85 - Milford Sound, NZ
86 - Dunedin, NZ
87 - Christchurch, NZ
88 - Wellington, NZ
89 - Napier, NZ
90 - Tauranga, NZ
91 - Auckland
92 - Brisbane, Australia
93 - Port Douglas, Australia
94 - Port Moresby, Papua New Guinea
95 - Lombok, Indonesia
96 - Klang, Malaysia
97 - Penang, Malaysia
98 - Phuket, Thailand
99 - Male, Malvides
100 - Cochin, India
101 - Goa, India
102 - Mumbai
103 - Mahe, Seychelles
104 - Mahajanga, Madagascar
105 - Cape Town, South Africa
106 - Durban, South Africa
107 - Dar Es Salaam, Tanzania
108 - Mombasa, Kenya
109 - Jiddah, Saudi Arabia
110 - Safaga, Egypt
111 - Elat, Jordan
112 - Port Said, Egypt
113 - Haifa, Israel
114 - Iraklion, Greece
115 - Kusadasi, Turkey
116 - Santorini, Greece
117 - Rhodes, Greece
118 - Mykonos, Greece
119 - Athens
120 - Dubrovnik, Croatia
121 - Bari, Italy
122 - Catania, Italy (Sicily)
123 - Naples
124 - Rome
125 - Venice
126 - Nice, France
127 - Marseilles, France
128 - Barcelona, Spain
129 - Eivissa (Ibiza), Spain
130 - Malaga, Spain
131 - Lisbon, Portugal
132 - Vigo, Portugal
133 - Saint Nazaire, France
134 - Le Havre (Paris), France
135 - Bruges, Belgium
136 - Southampton, UK
137 - Amsterdam
138 - Hamburg
140 - Copenhagen, Denmark
141 - Gdansk, Poland
142 - Riga, Latvia
143 - St. Petersburg, Russia
144 - Helsinki, Finland
145 - Stockholm, Sweden
146 - Goteburg, Sweden
147 - Oslo, Norway
148 - Edinburgh, Scotland
149 - Bergen, Norway
150 - Kristiansund, Norway
151 - Trondheim, Norway
152 - Tromso, Norway
153 - Hammerfest, Norway
154 - North Cape, Norway
155 - Longyearbien, Norway (Svalbard)
156 - Jan Mayen, Norway
157 - Akureyri, Iceland
158 - Reykjavik, Iceland
159 - Lindenow Fjord, Greenland
160 - Nanortalik, Greenland
161 - Qaqortuk, Greenland
162 - Goose Bay, Canada
163 - St. John's, Canada
164 - St. Pierre & Miquelon, France
165 - Sydney, Canada
166 - Charlottetown, Canada
167 - Quebec City, Canada
168 - Montreal, Canada
169 - Halifax, Canada
170 - Portland, Maine
171 - Boston
172 - Oak Bluffs (Martha's Vineyard)
173 - Newport, RI
174 - NYC
Quite the trip...I've done most of it twice. A few gaps here and there, but I know people who have been to all of these ports, and I think this would be a pretty amazing way to spend a year or two. I used to work on "The World", and they do this all the time. www.aboardtheworld.com.