Sow bear with cub, which is a bear you really don't want to surprise...
With the recent story of an 11 year old boy defending himself and his family from charging grizzly bear in Alaska, you might want to avoid bears. Stories like that make people want to see bears more.
The best opportunity to see wild grizzly bears in the lower 48 is either in or around Glacier National Park in Northern Montana or in or around Yellowstone in Wyoming. While it is not at all guaranteed to see grizzlies at either park, both parks have a relatively high population of grizzly bears and the bears in those parks (while still potentially very dangerous) are accustomed to humans being around. There are also lots of black bears in both those parks.
I'm your huckleberry...bears loves berries
Grizzly bears are the same species as the Eurasian brown bear. Brown bears, wolves and lynx are doing surprising well in Europe (amazing given, with the exception of Scandinavia, the human population densities are so much higher than the Western U.S. and Canada). Bears, wolves and boars in Italy do face challenges, such as bears being in isolated pockets. Similar issues are in Spain.
The eight species of bears in the world
Instapundit: One tree, 365 days (same tree in Italy I linked immediately above), Professional runner beats pair of bears (the safe bet is alway go hiking with a buddy, and make sure he or she is not as fast as you are)
CBC News: Oh Canada: The fight to save Bear 148 I know they mean well, but if you really want bears (as a species) to be able to survive in proximity with human beings, you need to be able to cull individual bears who become a problem with human beings.