Why is my green tea brown?
Hojicha is a green tea which is made from bancha, a low grade green tea, and cooked slightly; this very inexpensive green tea often comes out brown because it is discolored by oxidation. Other than this variety, and some very stale bancha, I can't think of a Japanese green tea that comes out brown. Some stale kukicha might come out brown, and low quality genmaicha made with poor quality kukicha could be brownish from the combination of excess oxidation and the toasted rice.

Most of the non-Japanese green teas I've seen sold as "green tea" and some lower quality teabags marked as "sencha" are broken down tea leaves that can easily oxidize in the packaging to the point where they are, at best, yellowish.

However, if you use even a moderate quality sencha, and it isn't stale, it should come out green. Most good quality kukicha and genmaicha will at least come out greenish-yellow. Since most Japanese restaurants use a fairly inexpensive second-harvest sencha, I imagine you're either buying hojicha or simply using a very stale, low-quality sencha.

Chinese green teas are sometimes slightly yellow, but if they're actually yielding a brown brew, they, too are either stale or are simply mislabeled oolong.

I used to sell a fair amount of green tea when I ran a small scale import business. I do recall even matcha products turning brown after being exposed to excessive sunlight; one of the bakeries I know was constantly running into issues with their matcha pound cake slices on sunny days, especially those pieces in the front of their pastry case. So it's reasonably possible you simply have tea which has been stored improperly; you're best off with a nitrogen flushed tea and it should be used within about 6 months of opening the sealed package. If your tea comes unsealed, it probably isn't in very good shape to begin with.

In any event, my recommendation is to try a first-harvest high-mountain grown sencha that is sold in nitrogen-flushed aluminum packages. Depending on the style, the brewed color will be either very green or slightly yellowish if brewed in the typical way. You can either do a very brief, several second infusion at near-boiling, or a longer infusion at around 80 celsius. I like it both ways.

Gyokuro, if you can afford it, is extraordinarily green, but is unlikely to be served at a restaurant without an additional charge (it's essentially the same leaves used to make matcha, except rolled instead of being milled).