Did late 1800's Japan have "tourist tat" (i.e poorly made items made for sale to unwitting tourists)?

They certainly did.

One interesting example is swords and knives with carved ivory or bone mounts. These vary in quality from excellent blades and fine carving work on ivory mounts through to low quality blades and low quality carving on bone mounts. (Low quality mounts don't always mean low quality blades - after the wearing of swords was abolished, some good sword blades were recycled for tourist sale in such mounts.) One example of a good blade in good mounts: http://collections.vam.ac.uk/item/O92912/sword-and-scabbard-muneaki/

These combine something Japan was famous for (swords) with something visually striking (the carving) and compact enough for tourist luggage (these were usually short swords or tanto (i.e., knives)). Similarly, late 19th century China produced many short jian (swords) as tourist tat.

These were made in Japan for tourist sale until WW2 (after which swordmaking was closely regulated). Post WW2 swords like this are usually made in China (and are still being made).

Clothing was also a common tourist purchase - colourful and visually striking, distinctively Japanese, and luggage-compact.

How would a Westerner travel to Japan at this time?

Travel was by ship. Many of the early Western travelers in Japan were there for business (government or commercial). The Japanese government started promoting foreign tourism in the 1890s, and the number of tourists increased. Many of the early tourists included Japan as one stop among many in voyages around the world, or as part of a longer visit to Asia.

For a summary of early Western tourism in Japan, see Roger March, "How Japan Solicited the West: The First Hundred Years of Modern Japanese Tourism ": http://www.inboundtourism.com.au/pdf/western-travel-in-japan-1868-1964.pdf