Hmm then I am going to suggest a Mojito - it's got lime, mint, sugar, a little
carbonation... Of course a Mojito (any drink really) can be made too strong,
or too sour, but a properly made one should be perfect. You can also ask for
it to made sweeter if you want to be on the safe side. You can also try a tall
daiquiri, but they may look at you funny, depending on what sort of
establishment you are in.
Mojito: http://www.webtender.com/db/drink/1435
This recipe calls for 2tsp sugar to about 1oz of lime juice, which is going to
be sour. I would use up to 6tsp of sugar and/or use lemon-lime soda to fill.
Daiquiri: http://www.webtender.com/db/drink/292
Again, this recipe is using 1tsp of sugar to 3tsp of lime juice, which I think
is going to be too sour - I'd go with 3/4 to 1oz of sugar/simple syrup.
Ordering it tall means they will fill it up with some soda water or 7-up,
which will soften the flavor.
If you want something more like just a blend of fruit juices, probably you
want something like a Pina Colada, Blue Hawaii, Hurricane...
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-If