FWIW -here are some of mine

Somewhere beachy for three days
You say you want three* days somewhere beachy between ORD and SYD. It sounds to me like you are time-constrained, which would mean a side-trip to say the Caribbean or S.E. Asia would eat too much time in flying. California of course has good beaches, starting with Venice Beach in L.A. You could fly home via SFO and stay on a beach somewhere there. Or on the Gulf Coast and fly home via DFW.

As I posted earlier, your proposed stopover in Hawaii should work. I checked on The Matrix and 1-way flights from KOA to HNL cost USD91

* Three days: remember you “lose” a day on the way home – by crossing the Date Line

The Global Explorer
This is Oneworld’s other round-the-world ticket. It cannot be purchased on-line, so you must either phone an airline such as Qantas or use a travel agent to buy it.
It allows more airlines to be used, including Fiji Airlines and Qantas codeshares on Air Tahiti Nui. So a stopover in either Fiji(NAN) or Tahiti(PPT) is possible.

It restricts the number of stopovers to 5, with no more than 2 in any region (the Oneworld Explorer has no such restriction).
So your stopovers would be HND, LHR, JFK, ORD or LAX, NAN or PPT.

If you are travelling in economy class, the Global Explorer is AUD600* cheaper than the equivalent Oneworld Explorer. If in business or first class, there is no price difference.

* Approximately AUD600 cheaper – the total price depends on the various taxes, fees and (sur)charges for different itineraries

Maximising the ticket benefits
These RTW tickets are not cheap – therefore I always try to get as much value of them as possible. So I have a couple of ideas in this regard. But first, I will list some relevant fare rules:

• You are allowed a maximum of 16 segments (either flight segments or surface segments]
• You are allowed up to 6 flight segments in North America and up to 4 flight segments in other continents
• You are allowed a maximum of 2 stopovers in your continent of origin
• You must finish up back in your country of origin, but not necessarily at the same point you started from (this is a simplification of the rule, but is correct for Australia)
• Travel may not be via the point of origin
• You are allowed 1 year from your first flight to complete your itinerary
• A second visit is allowed to Asia

First Idea – A holiday in Australia
Make your point of origin somewhere other than SYD (for example MEL or BNE); travel round the world and return to SYD (SYD will become 1 of the allowed 2 stopovers in the continent of origin)
Sometime within the ticket’s validity have up to 4 flights in Australia and one more stopover (any other ‘stops’ will need to be transits, meaning less than 24hrs). A sample itinerary is:
MEL-NRT-LHR-JFK-ORD-LAX-KOA,HNL-SYD-PER-BME-BNE-SYD

The Australian holiday could be before you leave on your RTW trip instead of after MEL-PER-BME-BNE-SYD-HND-LHR-JFK-ORD-LAX-KOA,HNL-SYD

Note 1: the online tool has a bug that enforces an old rule restricting stopovers in the country of origin to 1 before departing RTW and 1 on return from RTW (booking through an airline or travel agent will get around this)

Note 2: this idea will not work for the Global Explorer, only the Oneworld Explorer, because:

• Your South Pacific stopover (NAN or PPT) and your SYD stop will use up your 2 allowed stops
• The economy Global Explorer has a maximum number of miles allowed (26,000) and your itinerary leaves very few miles at the end. Business or First allow more miles (34,000) and you can pay more to get more miles on the economy ticket (but you are still only allowed 2 stopovers in your continent of origin)

Second idea – a holiday in Asia
Do as [MENTION=2110]R2[/MENTION] suggested and fly from the US back to Asia, have your beachy stop, and then
Fly back to Australia on a separate return ticket
Return to Asia sometime later and pick up the RTW ticket again; travel around there and return to Australia

Note 3: I did this some years ago on an ex-PER RTW ticket; the relevant part of the ticket was …LHR-PEK-HKG-SIN (cheap SIN-PER return on Scoot then, six months later) SIN-BKK-BOM-SYD-PER

Note 4: The first and second ideas can of course be combined

Third Idea - Start (and end) somewhere other than Australia
[MENTION=2110]R2[/MENTION] made this suggestion. Its potential benefits are:

• Lower ticket price (though offsetting this – you have to get yourself to the starting point and back from the ending point)
• Australia is no longer the continent of origin so there is no restriction on stopovers there, just the allowed 4 flight segments

R2 suggested starting in Japan because its prices for Business and First are lower than Australia (other Asian countries are similar to Australia).
These are the approximate savings on your ticket:
Economy – AUD850 more expensive in Japan!
Business -AUD2000 less expensive in Japan
First – AUD2250 less expensive in Japan
(The Aussie dollar has been falling in value lately, so these savings are not as good as they used to be)