My advice is dated, and from what I've seen on my most recent trip, the selection is far better than when I used to go there a lot. There wasn't shit there in the 80's, but it grew like a weed in the 90's, and now it looks like Dallas. That's north of the border...the other side has changed little.
It's been a while, but I used to go there frequently and I usually stayed at the Howard Johnson's (I suppose it's still there) down on the river, just west of the bridge...not the I-35 bridge but the walking across bridge, I think it's Convent Av. My company kept rooms there so I don't know the price, but I should think that it would be within your budget...and you can easily walk to the bridge from there.
The HoJo is on Ventura St, I think. You can't miss it because it's about 15 stories and the only tall thing around there. It has a fenced parking lot. Ask for an upper floor with the window facing the Rio Grande. (I haven't been near there during the last few times down there, this is old info, so check it out on the HoJo site or call a travel agent and ask).
Another good bet is to go to Google and type in "howard johnsons laredo tx". It should bring back a Google Map of Laredo - study it a bit - with links to several of Laredo's better hotels. I saw Marriott, Red Roof, La Posada, La Quinta, Holiday Inn, and Day's Inn, but if the HoJo is still there, you should stay there even if it's looking worn out, for it's convenience to the bridge, because I assume that you're only going to sleep there and spend the rest of your time chasing ho's in Boys Town.
The La Posada, Zaragoza at San Agustin, is also an easy walk to the bridge. Don't have a clue to the cost. Of course you will want to walk across the bridge and take a cab to BT. Just tell any cabbie Casino Papagayo and he will take you straight there for ten bucks...grab another guy with the same intent if you can and share...act as if you are together. Don't drive your car, the road is rough and you leave yourself open to potential disaster in case of a car wreck, even if you have arranged insurance for it...not worth it.