San Jose is a fairly safe city, so I wouldn't worry too much about safety - just use regular common sense like you would anywhere. I wouldn't plan on walking much after dark though except in the downtown core or around Santana Row (or other areas with a high concentration of restaurants, etc.). It isn't that anything is particularly dangerous, just that San Jose is quite spread out so there isn't a lot of pedestrian or bike traffic after dark except in certain areas. It isn't like some other large cities with a higher population density where you have people walking around at all hours.
The area around your hotel is fine - it is a mix of residential, commercial, and hotels - nothing of particular interest there though. The lightrail does stop in front of your hotel, so you can take that into downtown, to Mountain View, to Campbell. It runs fairly often and into the night, so you can get back to your hotel after dinner - I wouldn't hesitate to take lightrail alone at night - and since it stops in front of your hotel, it is quite safe. And taxis are also a good choice - they aren't cheap here, but they aren't terribly expensive - good if you want to get somewhere more quickly or if you are just uncomfortable alone on the lightrail later in the evening.
Here is a good site for estimating taxi fare: http://sanjose.taxiwiz.com/?lang=en
Santana Row has been mentioned - it is a nice area built maybe 10 years ago - restaurants, high end shops, condos and townhouses. The lightrail doesn't go there, so I would take a taxi - there are buses, but a taxi is easier. When the weather is nice, it is great for sitting outside for dinner and drinks. Very safe area.
Valley Fair across the street is a standard indoor shopping mall like you will find in any large city - it is a nice mall anchored by Macys and Nordstrom with all of the standard mall stores that you would expect. If that is the type of shoping you are interested in, then this is an excellent choice.
Downtown has a lot of restaurants and bars, not much for shopping - it is a direct shot on the lighrail from your hotel to downtown, so very easy to get to. A taxi ride would be fairly cheap too. If you are interested in technology, the San Jose Tech Museum is very good - it is right downtown. The SJ Art Museum is also there - it has some good exhibits. The library on 4th and San Fernando often has interesting exhibits too - this library is a joint venture between the city and the university.
I have to disagree with the recommendation for Original Joes though - it is a SJ institution and has been around forever, but I think they are resting on their reputation - it makes me sad to report that, but so it goes. I keep hoping they will revamp their menu, but they probably won't - the restaurant still gets a lot of business, maybe people going there out of habit. I have eaten there a couple times in the past few years and the food is quite bland - you would expect the marinara in an Italian restaurant to be flavorful, but Prego from a jar tastes better. There are tons of other choices - almost any type of food that you want to eat is available. I can give you some recommendations if you choose to go down there - just let me know what you like.
Mountain View is a bit farther away, but easily reached on the lightrail - direct train from your hotel. Castro Street has a lot of restaurants and shops and the lightrail stops right at the end of this strip.
Campbell is another good choice - also easily accessible on the lightrail - you would take the lightrail through downtown and continue onto Campbell, but you don't have to change trains, so it is easy. Campbell is a smaller town, but as with all the towns in this area, they kind of blend together at their borders. Campbell Ave has several blocks of shops and restaurants, a couple cool bars. It still maintains its unique character.