My favorite outdoor spots in no particular order are:
1. Mission Peak hike in Fremont. 2-3 hour round trip, 2,200 foot elevation gain, to the peak of a mountain. It's a tough hike up, but the views are amazing (sometimes the peak is above the clouds). I do this hike once a month, but I only do it on weekdays. I start when the park opens at 6:30am, and I'm done by 8:30am, and at work by 9 (I do hike it fast though). Parking at that hour is plentiful in the residential area around Stanford Ave in Fremont. Avoid weekends - it's a zoo.
2. Big Basin in Santa Cruz mountains. This park encompasses much of the Santa Cruz mountain range. I prefer to enter the park through Saratoga (southwest of San Jose). The road is windy though. The park offers campgrounds and is "full service", usually has enough parking, and has well defined trails and occasional waterfalls. These mountains are lush, so the trails are usually shaded. There are a number of trails of varying lengths, most are loops. For a really exciting hike, do the "skyline to the sea" hike from the mountains down to the pacific ocean near Half Moon Bay, and back. Actually, I recommend starting at the ocean, hiking UP, and then having the easy return down (this is a full day hike).
3. For something a little easier and closer, Fremont Older Open Space Preserve in Saratoga. This is probably the closest park to us that I consider to be hike-worthy. There are a number of trails, varying lengths, most are loops. There isn't much shade here so bring a hat. Parking is also quite limited, so go early in the day.
Trivia: The trails I mention in #2 and 3 are connected. In fact, most of the trails that exist from Santa Cruz, up through the Santa Cruz mountain range, through west San Jose, up to the Los Altos Hills (west of Mountain View) are all interconnected. I have never hiked between parks though - I usually stick to loops within a park.
4. Stanford Dish hike. Starts near Stanford University and goes up a moderate, unshaded incline path to the Stanford satellite dish. This is a 1-2 hour fairly easy hike, good for a picnic, etc. Parking can be limited around Stanford.
5. Alviso. Basically a section of North San Jose, and the headquarters of Tivo. Drive up to Alviso Marina County Park, park there (plenty of parking in the park or on nearby streets), and explore the ghost town, and the trails that loop out into the marina / bay. Great photography here. walk around the streets of the town just south of the marina and inspect the abandoned buildings from the gold rush era. You can easily spend 3-4 hours wandering around taking pictures. Twilight / before sunset is really nice lighting. Watch for the Amtrak and other trains going by - also great photography opportunities.
5. Stevens Creek Trail, Mountain View. This trail goes right by the main Googleplex, down into Cupertino. It's a paved trail, really meant for bikes, but if you just want to get out and about this can be fine for walking. If you have a bike this is really a great trail to ride. Especially the north part near Google, it connects into Shoreline park and even goes north along 101 into Palo Alto area. The whole trail is fun to ride around - lots of wildlife, marsh areas, etc. I do recommend biking this though - it's a long flat paved trail that isn't much fun for walking. One of the better biking trails though. There are similar paved biking trails that stretch from Google basically all the way down to South San Jose, and even further south to Milpitas and Los Gatos. They're very enjoyable if you're into flat, paved-path biking, but they're really not enjoyable for walking/hiking.
Unrelated to hiking, a few really nice places to visit and explore:
- Half Moon Bay, and the Public Access Beach next to the Ritz Carlton. Beautiful.
- Alviso, mentioned above
- San Jose Japantown. Good spot to go for lunch or dinner, and walk around and explore the area. It's an up and coming area of the valley.
- Computer History Museum in Mountain View.
- Stanford University campus