Why Third Party Reservation Websites Are For Chumps
First, virtually every hotel has a lowest-price guarantee if you book directly with them, and they will all meet or beat the third party rates. Why? Because those sites take huge commissions out of the rates the hotels set, and the hotels would obviously like to hang on to those funds. Generally, third party sites take their commissions before making the actual reservations with the hotel, which means the "real" rates on third party reservations (which are confidential and never appear on guest bills) are usually the lowest in the hotel. And they're often treated that way, although I'll get to that below.
If you're looking at an air/hotel package that seems to be discounted below what you'd pay buying air and hotel ala carte, break it down by looking up the fare for the exact flight on the airline's website. Hotel rates are much more changeable than air fare, so it's likely the package's "discount" is being absorbed by the website and probably the hotel. Once you have the airfare figured out, you can subtract it from the package rate to infer what the hotel-only rate should be. Call and ask the hotel to beat that rate (if you don't have success with reservations, try the front desk). The hotel would always rather sell directly to you, even if they have to undercut their own "Best Available" rates to do it. Almost any discount they offer you is a much lesser hit than the commission they're paying out. And who knows? Hotels often offer certain club members (AAA, AARP, American Express card members, etc.) even deeper discounts.
Booking directly with the hotel has many other advantages, though. Most third party sites have very inflexible cancellation and modification policies in that you can't do either. Those policies are generally contracted so that the hotels are hamstrung and simply cannot modify the reservations from their end. So if you book with a third party site, you're committed. They're big, anonymous businesses, so it's virtually impossible to get refunds when you change plans. Good luck getting some call center drone to sympathize with your not being able to travel due to a sick child or an impending hurricane. They hear dozens of such calls every day. Even if you get somebody who'd like to help out, they are often restricted by their software from doing so.
Hotels, on the other hand, usually only require that you cancel at least 24 hours before scheduled arrival, and modifying your reservation, even during your stay, is very often penalty-free. So why tie yourself to inflexible travel plans if you don't have to?
Oh, and if your stay wasn't everything you expected, there's nothing the hotel can do to compensate you on your room and tax, because you paid the third party site, not the hotel. The hotel literally doesn't have your money, and there are a lot of complicated contracts with the third party sites that prevent them from getting it back to you. Higher-end hotels will often do whatever it takes to make a guest happy before they check out, including comping nights or the entire stay, if the complaint is egregious enough. You don't want to prevent them from being able to do that for you.
Last, there's a subtle and often not-so-subtle discrimination by hotel employees against internet travel guests. First, internet travel guests simply do not bring in the same revenue as regular guests, due to the extremely high commissions. Second, they are most often single-stay tourists, unlikely to be returning to the city, so there's no motivation to 'wow' them to come back. Third, by demonstrating that they comparison shop for their travel, they've indicated they're unlikely to be loyal to the brand or the hotel even if they do return to the city. There's not as much motivation to offer perks like special occasion amenities or free upgrades.
Also, the blunt truth is, when a hotel is nearing maximum occupancy, the better rooms will be held for more valuable guests, and internet travel guests will be blocked into the crappiest rooms. It just makes good business sense to give preferential treatment to the business guests and high-end tourists in order to woo them to return. You may not be not guaranteed the best rooms if you book directly, but at least you won't be earmarked during the arrivals process for the less desirable rooms.
So, in closing: Booking directly with the hotel will get you better rooms, better service, more flexibility with your travel plans, and it costs less. By all means, browse those third party sites to comparison shop; just don't actually book with them.