I can't speak to Hazel at all, but I've seen a few people post that Homewood is not exactly the safest station around and I think I've even seen a news report or two about crime in the parking lot at Homewood. So I'd be careful about going there.No personal experience with this yet, but we are trying to put together a low-budget Chicago trip once the HSR segment starts up in July. We have found several no-frills type hotels (Super 8, Knights, Travelodge, etc.) around the Homewood/Hazel Crest area. Depending on your travel dates, they go for $30-60. Metra serves both towns, and several of the hotels are within walking distance from the Metra stations. From what I understand, it's a decent suburban area (though correct me if I'm wrong; when I used to have family in Chicagoland, they were in the NW suburbs). Metra Electric line runs you $5 each way to get to Millenium Station, so it's not a bad deal even considering the extra cost.
Perhaps someone from the Chicago area can comment further on this and that station's safety.