There we go... I wondered why the Mirage and Aria weren't on the previous list.
I reckon the Aria might be a better bet than the Bellagio simply because it's newer, those are basically the two high end properties
Technically the MGM Grand does have two additional hotels within it that are super high end - their skylofts on the roof and the Mansion... these are rather $$$ (the mansion couldn't even be booked until recently but was a perk for legit whales via their personal casino hosts only).
For your cheaper - mid range hotel day (these aren't "low end" btws... the low end strip hotels are owned by Caesars (formerly Harrahs) and there are even lower end options north of the strip - they had the worst one on the strip: Imperial Palace (now refurbished and rebranded as the Linq and other budget options)). I'd consider the Mirage, it used to the the high end MGM property before the Bellagio and Aria were built (like the Bellagio it was built under Steve Wynn... who then went on to open his own hotel... the Wynn) as it has a nice location.
Can you get the Vdara - it's basically right next to the Aria and is a condo hotel (as in some of the rooms are privately owned and let out by the owners via MGM) - IIRC you can use the Aria pool etc.. (best check this though) as well as Vdara. It's potentially a useful option as it doesn't have a Casino and all the other stuff to faff about with - you should have an easier time just checking in and going to your room.
Also perhaps worth a look - the MGM Grand also has a "condo hotel" on the property, which for similar reasons to Vdara might be of interest - it's called MGM Signature.
In both of those cases, as they're condo hotels, you'll either have a studio type room or a separate bedroom and living area/kitchen... so you'll have a proper fridge (not just a hotel room fridge with overpriced drinks in it etc..). I'm not suggesting you need cook for yourself on holiday etc.. but it's sometimes nice to have say some milk. breakfast cereal etc.. and just a bigger room/lounge area etc... Hotels in vegas are massive so popping down to breakfast isn't exactly just popping down...
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Also just a random Vegas fact to point out to anyone else - not relevant to MLife rewards as not an MGM property but there is a little known condo hotel right next to the Bellagio... it's old and is owned by the condo owners... thus they couldn't sell it knock it down without agreeemnt... so when the Cosmo was built they literally built it around this hotel (including taking over the parking lock)... Why mention it - well just because it's quite a random little hotel and quite quirky - because of this arrangemnet with the Cosmo if you stay there then you actually get access to the pools at the Cosmo itself... there is a lift from this little hotel that takes you to the Cosmo... also because it is right next to the Bellagio you can get a room with a fountain view! It's also codnos so you get a kitchen etc.. It is not however high end - it's just the budget/location/unknown aspect that is cool.
^^^^ It's like the hotel version of one of those old folkes who holds out and refuses to sell to a devloper despite being offered huge sums of money.... so they end up building around it.