Is there a reason why you are not considering the Hilton Ras Al Khaimah Resort & Spa in RAK? I think it's Hilton's nicest beach property in the UAE and it prices up around the same as the other RAK beach properties. (It doesn't show up when you search for Dubai properties as it is a little further away from DXB than the Al Hamra and Marjan properties but is worth the extra 15 minute drive if you go for the RAK option.)

Both of the Jumeira properties are adjacent to active construction sites if that bothers you - still quite hard to avoid this in Dubai.

If it was me I'd do 4-5 days in RAK and then splurge on either the Conrad or the W=A in DXB for a couple of nights (would still end up within 1000AED a night on average)

Agree with DanielW that the view of the fireworks from the JW Marriott Marquis will be good but would add that the surrounding area is not particularly pedestrian friendly - you would struggle to walk into the Down Town / Dubai Mall area for example.