Siberian Thrush is a skulking migrant through the area, I come across them on the hills around Kyoto in late September and October but in lower numbers than the other migrant species. I can't recall ever seeing one in the city parks but they certainly turn up in the larger Osaka parks. Eye-browed is usually the first autumn migrant to arrive and can be quite common in September, as can Japanese and Brown-headed. These turdus migrants are common in the hills but can be quite easy to find in Kyoto parks too. Fruiting trees next to a pond at the northern end of the Imperial palace Park is a good place to try. Japanese is also a common breeder in the mountains of Kansai. Pale Thrush arrives in autumn too and remains a common feature of the winter birding landscape in Kyoto parks and the surrounding hills. Dusky Thrush is another winter visitor though it doesn't usually become common until mid-winter. The first birds tend to stay in the mountains, later becoming common in open country as the weather forces them down. Naumann's occurs in winter but it's very uncommon and hybrids are just as likely, if not more so. Hegura in October is a good bet for Naumann's. Coming back to zoothera, White's is widespread in low numbers in winter and can be found on hills surrounding Kyoto, sometimes they even winter in the Imperial Palace Park but tend not to linger so long in the botanical gardens. When weather is hard they can become fairly common in the open along roadsides around northern Lake Biwa. Other species are vagrants in the region, Red-throated, Black-throated and Fieldfare have all occured in Kyoto or Osaka the last 20 years. Still waiting for Redwing!
Spring passage is more urgent and though the same places are good to check more luck is required to be in the right place at the right time. Brown-headed Thrush (along with Pale and Dusky) can be particularly common in trees along the Uji River and is the only migrant I see more commonly at this time of year compared to autumn.
One of several White's Thrushes seen on this date around northern Lake Biwa, 18 February 2008.
This bird was in Kyoto botanical gardens, 3 February 2013.
Spring migrant female Japanese Thrush on Mishima.
An interesting bird which seems to be a 2CY female-type male Japanese Thrush on Mishima, 2 May 2010.
Male Eye-browed on Hegurajima, October 2007.
Eye-browed Thrush Ogura, Kyoto 3 April 2014.
Pale Thrush is common in winter and they can be very confiding in parks. This one in Kyoto botanical gardens, 7 March 2012.
Male Brown-headed Thrush on the Uji River at Ogura, April 2014.
Female Brown Thrush in the Palace Park, Kyoto. Dog walkers and joggers start early and birds soon disappear into off-limits areas.
Female Izu Thrush, 17 May 2013. 
Black-throated Thrush very briefly in the botanical gardens Kyoto, 5 December 2012. I must have been the sole observer for this one.
A Naumann's Thrush on Iriomote 3 April 2013.
Naumann's Thrush, Hegurajima October 2014.
Spring male Duskys are stunning birds, this one on the Yamato River, Osaka.
Dusky Thrush Matsusaka, Mie 20 April 2014.
A more typical mid-winter bird, 17 January 2011.
Dusky (rear) and Dusky x Naumann's hybrid, Ogura 13 April 2011.
The same Dusky x Naumann's hybrid.
Fieldfare on the Uji River 18 February 2009. Very obvious moult contrast in the coverts. 
Song Thrush in Kanagawa 7 March 2014.
Mistle Thrush, 21 February 2014.