The Omni seems like a very nice hotel, at least from the outside. It's in the middle of the Financial District, so it's safe around there, but most of the small businesses in the area cater to the office worker crowd. That's OK if you're interested in happy hour or a sit down meal, but generally boring for sightseeing. Chinatown and the North Beach neighborhoods are close by and would be interesting to walk around. The streets of Chinatown can get packed with people on the weekends. One of the cable car lines passes about a block from the Omni. I think that particular line heads towards the Embaracadero. That's a mall (nothing special for a tourist) and you can see the Bay. I forget if you can see a bridge from there--either the Golden Gate or the Bay Bridge.

The only area I would steer you away from downtown is the Tenderloin district, but that's a ways from the Omni and there's little reason for you to head that way anyway. Just be aware of your surroundings and you'll be fine anywhere you're likely to visit on this trip.

Yes, check the weather before you leave. They had 25 days of rain in March and still going strong in April (I was there for about 7 of those rain days). Make sure to take a wind-resistant outer layer regardless of the forecast. San Francisco is temperate, temperature-wise, but that ever present damp ocean breeze makes it feel much colder than the thermometer indicates. People from "cold" regions often complain about how cold they feel in San Francisco, even on a 55 or 60 degree day!

It's a beautiful city. Of course, there's a not-so-perfect side to it, like all cities, but enjoy the good parts and forget about the bad parts. Cheers.