The New York Times site has issues from 1854 to date (subscription), but members of the Bergen County Cooperative Library System (BUCKLES) have free access.

The reference Fred is seeking is: "Readers' Guide to Periodical Literature", H.W. Wilson Co., which has been published since the early 1900s. It covers articles from about 400 popular magazines which are listed by author and subject matter. It is published monthly and the issues are combined into a yearly volume.

In Montgomery Co., MD, a complete set is available at the Montgomery Co. Regional Library in Rockville. I do not think an on-line version is available. Subscriptions are about $500.00 a year. There are other guides such as Index Medicus, Biological Abstracts, Chemical Abstracts, but I think these would be of little use. I do remember that Index Medicus had a section on Medical Numismatics.

As long as "Old Magazines" means 19th century publications, I've found that Google has digitized bound volumes of publications such as Hunt's Merchants Magazine and many others (although given Google Books' "clunky" search mechanism, I usually have an easier time finding the available bound volumes at HathiTrust.

I also like to use the Making of America sections of the Cornell University and the University of Michigan library websites. They have such magazines as Harper's Monthly and The Democratic Review (Cornell) and DeBow's and Southern Quarterly Reviews (U of Michigan).

The last time I checked, several years ago, Harper's Weekly was still only available via CD, which was available for purchase.