Good quality LCD tuner for tuning in sunlight?

I think any LCD display might be difficult to see in sunlight too. You could try your luck with an analog guitar tuner that has a real needle instead of a digital display.

(Aside: I just did a lot of reading, during which I discovered awesome guitar videos on PlanetWave, which also makes tuners.)

As for the tuner, given your likely budget and stated needs, the following seem a good fit. They all have a back-lit screen and clip onto your instrument.

• The Joyo JT-22B popped into my head when you mentioned sunlight. It took some time to find, since I had only seen it once (a few weeks ago, in Wales, of all places, on a ukulele---OK, too much info). However, the results only come up for sites in the UK and Australia. This makes me wonder if Joyo sells under another name in North America. (See the Google results for Joyo JT-22B)
• The Korg 20AW-2G costs about $30; it has a clip, a wide screen, and a color LED backlight.
• You could also take a look at the Intellitouch series. They are diamond-shaped, they clip on, and are smaller than the Korg above.

Update:

• I found the company's website. You can look at their tuners here. They also have multi-functional tuners (e.g. with LED flashlight and metronome), but I can't seem to find their products on the US Amazon site.

A good guitar player always carries a towel. The towel goes over your head. It will block the sun. Towels are cheap and you can sneak one out of the house when your Mom is not looking. You never see people in the Middle-East with tuning problems.