Staying for 7 days should make it easy to average $100 per night, if that is okay with you. So under $700 for the entire week.

My pick for the best bargain on the strip is either Harrah's or Flamingo, but only if you pick one of their recently renovated rooms. The Caesar's website makes it easy to choose a renovated room and I think they are great for the price and location. Obviously, YMMV.

Both of them have a great central location, easy access to the monorail, walking distance to lots of interesting attractions, easy bus/taxi/Uber options. The renovated rooms are sleek and comfortable. IMHO the weakest link is the restaurant selection, but if you don't mind walking around the strip a little you have a good selection nearby.