I need to get Hawaii for Worked All States, and live on the East Coast (Virginia). Furthermore, I have a poor antenna, and thus only the prime times of the day seem to really be opened for me. What time of day/band is the best to make the QSO?
Here's a propagation prediction made using PropView with the VOACAP engine; the thicker the line the higher the probability of an opening:
As you can see, your best bet on the higher bands is 10m between 18Z and 23Z, followed by 12m around 18Z, and from 22-24Z.
On 40m and below, both ends of the path between you and HI must be in twilight or darkness, which as the screenshot shows means 4Z to 12Z.
Signal paths that parallel the solar terminator can be enhanced by "greyline propagation", but your QTH is too close to Hawaii for that.
In general, my experience is that band conditions are best for long-distance communication at sunrise and sunset. You generally want the sunset to be somewhere in between you and the person you are talking to, so probably something like 9 PM EST.
Beyond that, things like solar weather can make a big difference. I tend to use VOAProp for predicting when and on what band I can best make a contact. The ARRL also publishes propagation charts that show the best time of day. Their November 2013 chart shows that the best time is between 1600 and 0000 UTC, which is noon to 8 PM. Finally, voacap.com has an interactive web tool that can give you propagation predictions.
Finally, remember that power and spectral power density make a big difference as well. 1500W on CW will propagate much farther than 10W on SSB. During good propagation conditions, however, 10W may be all that you need.
By my read of http://spacew.com/www/realtime.php it seems as if 10m could be open right now from Virginia. (Virginia, which is a big state, as compared to Rhode Island or Washington DC (not technically a state, but a tiny pin-point on the map))
Your great circle distance from Washington National Airport to Honolulu International Airport is almost 7800km. (calculated here: http://www.gcmap.com/mapui?P=DCA-HNL) As the Space Weather page explains, the MUF prediction is for a 3000km path (multiply MUF by 1.1 for a 4000km path), which means you'll have to look for the midway points and hope that your signal bounces an extra time. Looking at the two midway points, I see that the MUF is just about 33MHz.
For a quick peek at what may very well be possible, you could look at the propagation predictor on the home page of http://qrz.com
Do remember that this is all "prediction" - this is an experimental service so you must experiment! In ham radio, there are no substitutes for listening or transmitting (on an open frequency!). Often, you may find that you think a given band is dead, but once you call CQ a few times, someone else you haven't heard yet will pop on and tell you that he's in the middle of a conversation with someone else you can't hear. If you're lucky, the station within earshot will have a conversation or at least a contact with you once he's done with the other fellow.
Many other factors affect your ability to make that contact: Are your antennas radiating in the correct direction? Is anyone listening? Are you scanning the bands to see which stations you can hear and where they're from? Are you calling CQ? If no-one is listening, you won't make a contact. If your antennas aren't right, you won't make a contact. If the conditions aren't right, you won't make a contact. If you don't call any stations, you won't make a contact.
Start with the ARRL propagation forecasts. These are updated every month and there is a specific forecast for the path from the East coast to Hawaii.
For a customized prediction, use the online VOACAP propagation predictor here:
Finally, you may want to check in with the 3905 Century Club nets. Those are on several bands at several times per day, and are dedicated to WAS and similar awards.
I can only add the perspective as to when I had a phone contact with KH6LC on 11/17/12 @ 22:24. I made the contact with 12W on 10m, I believe it was during ARRL November Sweepstakes contest. That's likely a really good bet, a lot of stations get on the air around that time. I'm hoping to snag AK as it's one of the remaining few that I need for my WAS.
Besides monitoring spotting sites for KH stations, you might try contacting when you know there are a lot of Hawaiian stations working the band and where they are working it. Two sources to consider. One is the Ohana Net which is on the air regularly on the 20 meter band and I hear them all the time (but, I am in Washington state). They have a web site where you should be able to find the times of their net schedule. I think they are Saturday mornings: http://www.ohananetradio.com
Another source is the Hawaii QSO Party which does not occur in 2015 until August (at least it is in the future for 2015). I think it is August 22nd but check their web site which is at: http://www.hawaiiqsoparty.org.
You might e-mail some of the KH stations you can find on these web sites to set up a schedule. I remember in my days to fulfill my WAS I was lacking Rhode Island. After several years of missing it, I finally arranged a schedule with a guy in Rhode Island and then added my 50th state. So, schedules work even though they might be the last resort.
Depends on the band. You will have better success on 80m or top-band after dark. 20 will get you good DX all through the day, and 40, depending on conditions is good to ~1000km
You don't mention where in the US you are.
The current solar conditions indicate that 10m should get good results right now too.
Over the last 24 hours, 5 Hawaiian stations were spotted by stations on the US East Coast:
KH6OO on 30m at 0515Z
NH6I on 10m from 2135Z to 2142Z
KH6QR on 10m from 2134 to 2250 Z
KH6L on 10m at 2225Z
KH6SAT on 12m at 2309Z