I think the safest hotels are going to be on the opposite side of the freeway in the downtown area. They are most likely more spendy but worth it to be in the safer area. Plus there are restaurants and the park on that side.
It's pretty close to the light rail so you could stay at some place near that and just take the train.
Anywhere in the downtown area is a safe bet.
I've found that hotels in or around downtown town are the most expensive. I would suggest one on the outskirts. I would for Sapphire Inn & Suites in Channelview. The rooms are newly remodeled and the price isn't too expensive. Remember that, in Houston, the cheapest isn't the best option.
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