To add to all the good previous pieces of advice you were given before, you may be looking for monthly data on Tourist nights and tourist arrivals in European countries, there is a rich database on the Eurostat web site (http://ec.europa.eu/eurostat/data/database). You can simply click on "Industry, Trade and Services", then choose "Tourism" and "Monthly data ...").They are free of charge.
Monthly free of charge data are also published on the Spain's INE (http://www.ine.es/dyngs/INEbase/en/categoria.htm?c=Estadistica_P&cid=1254735576863) and on Italy's IStat websites (http://dati.istat.it/?lang=en&SubSessionId=da4f9019-537f-4558-8798-1708425d6776&themetreeid=-200) then choose "Services" and "Tourism".
As far as Italy is concerned, the Bank of Italy publishes monthly free of charge microdata on inbound tourism receipts and nights (https://www.bancaditalia.it/statistiche/tematiche/rapporti-estero/turismo-internazionale/distribuzione-microdati/index.html). It is based on a survey based on monthly interviews at frontier points and it should also have quality answers on the degree of satisfaction of inbound tourists with the areas visited in Italy.
If you need further info on all the above, please contact me.
It depends on which countries, regions you are looking at. The answers above mentioned different sources, but you need to specify first your countries/regions of interest. One important source is indeed the local tourist bureaus or the local statistical offices. Also, particularly in the case of small islands, central banks could be an additional source for statistics on tourists.
Some countries also have cruise tourism, and, therefore, you need to be specific as well on what type of inbound tourists are you looking at.
In case of Japan, you can find inbound tourists data on the site of the Japan National Tourism Organization (JINTO) (http://www.jnto.go.jp/jpn/). Most countries have tourism related agencies or departments which compile monthly tourists' data.
for Italy please have a look to ISTAT database (http://dati.istat.it/?lang=en, “Services”, “Tourism”, “Monthly Data”), you'll find informations regarding type of accomodation, residents by region of origin, country of origin and type of locality.