Lake Arrowhead is the mountain day trip I would suggest first from San Bernardino. The distance is short enough that you can leave the valley after breakfast and be among pine trees and mountain scenery surprisingly quickly.
The drive is part of the attraction. You climb sharply from the Inland Empire, gaining elevation and watching the urban valley spread below.
What to do when you arrive
Lake Arrowhead Village is the obvious first stop for shops, food and views toward the lake. Keep expectations realistic: much of the shoreline is private, so this is not a place where visitors can simply wander around every part of the water.
I would combine a village stop with a scenic drive or another accessible mountain activity rather than making shopping the entire day.
Weather changes everything
In summer, the elevation can provide welcome relief from valley heat. Winter can bring snow, ice and chain controls. Always check current road conditions before setting out.
Weekends can also be busy, particularly when fresh snow draws Southern Californians uphill.
Why it works from San Bernardino
The dramatic change of environment for relatively little driving is the main reason. You can spend the morning exploring Route 66 and the afternoon looking down through pine forest toward Southern California.
Few city breaks give you that contrast quite so easily.