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The Chase travel portal runs off of Expedia. If it's bookable there, most are also bookable through the Chase portal. Exceptions being all things Disney are blocked and most vacation rentals are also blocked. If you get the Chase Sapphire Reserve, you get 1.5 cent per point redemption through the portal. The Sapphire Preferred and Ink Preferred (business card) gets 1.25. These count as third party bookings and usually won't count towards hotel status.
With the Amex Hilton Aspire, you can get Diamond status. It comes with a free night for any standard room soon after card opening and again every anniversary. Diamond status will get you lounge access at certain properties, breakfast, and upgrades but it's based on availability.
With Hyatt, you can book suites using more points. You can get to Globalist status with 30 nights this year, which is half the usual required. You would get free breakfast and upgrades on availability. With 50 nights, you can get suite upgrade certificates, which would guarantee the upgrade. The Chase Hyatt card gets you 5 elite nights every year. URs transfer to Hyatt 1:1 if you have one of the more premium UR cards (CSP, CSR, CIP).