There are many threads on these, which you should read given that you have a lot of considerations. I have stayed at every Hyatt in town so can give some basic overview points.

None of the Hyatts (except the Place locations) have much "partying" in terms of areas to easily walk to from the hotel. The Centric is the closest, at La Mer, but I understand that some of the venues at La Mer will be closed or reduced in operation during the summer, and this is more of a family-type area anyway, with most of the restaurants and bars just phoning it in.

The Park is the only hotel, in my opinion, that is above-average for its brand and a standout in Dubai. It's really an excellent property and a steal at that rate. Breakfast is among the best in Dubai, the the pool/beach areas provide plenty of recreation (though I despise the noisy Twiggy "day club" that takes over a lot of the area). The hotel is isolated in a part of town that's not too interesting. But for a first-time visitor to town, at that price, you should definitely take advantage.

The Regency in Deira is probably my second favorite. The rooms are comfortable, F&B strong, Regency Club good, and elite recognition excellent. I often stay there in the $50-$70 range. You stand a good chance at getting a suite. But the location is not good in my opinion, in a far corner of Deira with bad traffic and difficulty to get a taxi/Uber at the location though there's a Metro stop close by. (Traffic used to be not so bad in the dead of summer, but Dubai is not as slow in July-August as it used to be.) I like Deira in general, though, for walking around and visiting local restaurants and dodgy bars if that's what you want to do. You'd still have to take a taxi (or a very ambitious walk) to get to the central Deira areas.

The Grand is also a good value, thought not an interesting area. I think the club is still closed, substituted with meals and drinks in the buffet restaurant, and you have a good chance for a suite upgrade. The rooms are comfortable and restaurants here are pretty decent, bars less so. It's a typical Grand Hyatt, of the dated (or classic, depending on your point of view) variety, not a bad choice at those rates. Given your objectives, there's really no reason to choose the Grand over the Park (in the same general area, visible right across the Creek) for relaxation.

The only sure thing is to avoid the Regency Dubai Creek Heights. It's a grim area with shambolic service and basic amenities -- though the Globalist offer, meals in Tablita, is good.

The Andaz is a sleepy property in a sleepy area, the Palm, though attractive in design as you'd expect. The Palm is OK for relaxing, and close to the more action-oriented area of Jumeirah Beach, a short taxi ride away. The waterfront restaurants across the parking lot are OK, and there are some other isolated nightlife areas on the Palm. It can be inconvenient to get on and off the Palm, though less so in July.

Splitting between the Centric and Park -- with Park for your resting and Centric as a base to explore the city -- would probably be the best overall experience though at the upper end of the cost permutations. You could substitute the Hyatt Place Jumeirah for the Centric to save a few bucks and sacrifice room comfort; it's an OK area not too far from the Centric with decent on-site F&B and plenty of other stuff nearby (plus Dubai Mall and Business Bay reasonably close). If you wanted a third stay on the cheap, you could try the Hyatt Place Al Wasl for a mix of the old Dubai and Deira nightlife -- a more urban experience.