I am an Indian man planning to travel around Estonia for a couple of weeks as a tourist. I would be covering Tallinn, Narva, Tartu, Parnu and perhaps one of the islands. I will be travelling alone, backpacking and staying in hostels. Is there danger of racist violence or any form of passive racism (i.e. preferential treatment of white people over black) that I am likely to experience? Are there areas I should be avoiding? I speak English very well, but no Estonian, although I am planning to learn basic words for daily use. Although I am Indian, I am from the south of India and have often been mistaken for being black or of African/American origin whenever travelling abroad. (And not in a bad way, if you know what I mean :-)) I also have prominently visible tattoos over my arm, non-religious and I don't know if they associate this with something specific there? Any inputs or advice?
I'm Indian, have lived in Russia and travelled to Estonia (and a lot of towns in the interior of in the former USSR where few foreigners visit). I have not experienced racism of any kind. In my years of travel in the region, if there were a few instances of unfriendly behavior, it invariably involved young men who had a lot to drink. You should be able to manage with English.
There exists racism everywhere on the planet, including in Estonia.
Hans Glaubitz was ambassador from The Netherlands to Estonia between 2005 and 2006. He is married (or at least was at the time) to a male black Cuban artist (at the time, there were only four countries and one US state where same-sex marriage was legal). Within a year, he left due to, what he said, homophobic and racist bullying against him and his husband. However, gossip claims that he was himself behaving snobbishly and that the hostility was rather a consequence of snobbish behaviour than of him being black or gay, or that his husband was simply bored with living in Tallinn and more than happy for Mr. Glaubitz to be placed in Canada instead.
This was in 2006 (12 years ago when I first wrote this answer), and it's quite possible that the incidents were exaggerated at the time and/or that racism (and homophobia) have reduced since then.
Disclaimer: I'm estonian and live in Estonia, thereby my view may be quite subjective.
In general, you should be safe. Most people here do not share racist views, although in light of recent years migration crisis in Europe some people have started hate every other human being, having different color of skin or different (esp muslim) religious views - likely same in other European countries.
Probably you should avoid night streets of bigger cities, where drunken young men just look for opportunities to harass someone. Well, I would not walk there myself either.
Otherwise learn few words of estonian (like Hello! - Tere!, Thanks! - Aitäh!), be positive, helpful and likely you win hearts of most local people. Due to the our history (forcefully migrated eastern workers didn't learn single word of estonian for 20 years) few estonian phrases should make wonders :)
Having recently returned from Estonia and having traveled around the country solo, without knowing the language, I am happy to report that with the exception of the immigration officers, my experience has been completely positive. It is true that people in this part of the world just do not smile and are not gregarious and outspoken, like you might expect in India or the Americas, but they were all very polite, well behaved and helpful whenever needed. No trouble or racism at all.
,,,,Racial disrimination here everywhere; in communication and in relationships and even in clubs. They give you small glass than local and citizens. I have lived in Tallinn for five years; people have attacked me every where and even in hospitals and everyone is going to insult you if you do not understand russian and estonian language. Someday I asked one women her number what do you imagine?, she gave me man phone and asked her friends to follow me then attacked me physically and when I asked police they even did not follow them almost they did nothing and moreover; their body gestures said they were very happy that some locals attacked foreigner and make him many bruises. I have much to say about my adventure among these racist citizens and locals. You free to try but be quite sure that police here only appearance no one will protect you or any properties belong to you Good Luck)