Is there a good and objective resource online about Zika virus?

It doesn't get much more impartial or authoritative than the World Health Organisation (WHO), and they keep clearly written, regularly updated pages on Zika.

For travel, I recommend their excellent Q&A document. In particular, note they don't advise against travel:

To protect against Zika virus and other mosquito-borne diseases, everyone should avoid being bitten by mosquitoes by taking the measures described above. Women who are pregnant or planning to become pregnant should follow this advice, and may also consult their local health authorities if travelling to an area with an ongoing Zika virus outbreak.

Based on available evidence, WHO is not recommending any travel or trade restrictions related to Zika virus disease. As a precautionary measure, some national governments have made public health and travel recommendations to their own populations, based on their assessments of the available evidence and local risk factors.

So the American government's advice to not travel is not endorsed by the WHO.

Their "factsheet" page is also a good place to get a level-headed take on the basics.

Then their zika homepage contains news and updates, which is useful for a disease where there are a lot of uncertainties, discoveries and new developments.

The BBC also have sensible, sober travel advice.

One thing I would suggest travelers note, is of you do get Zika and are ill in bed with a fever and joint pains - or, perhaps more importantly and more likely, you get Dengue Fever and are ill in bed with fever and horrible joint pains (my bold):

Take medicine, such as acetaminophen or paracetamol, to relieve fever and pain

Do not take aspirin, products containing aspirin, or other nonsteroidal anti-inflammatory drugs such as ibuprofen

Get lots of rest and drink plenty of liquids

Prevent additional mosquito bites to avoid spreading the disease

The latter drugs might risk haemorrhage. This is a known risk for Dengue Fever, I don't think it's proven yet for Zika (so CDC publish this advise but not yet WHO) but the two are closely related so it seems like a sound precaution.

In short - pack light long-sleeves, plenty of high quality mosquito repellant, and paracetamol.

They also address your question about sexual transmission:

It is thought the virus can persist in semen for two weeks after a man recovers from an infection.

Public Health England is taking a safety-first approach after two suspected cases of sexual transmission. The organisation says the risk of spreading the virus through sex is "very low".

But it recommends using condoms if you have a pregnant partner or one who might become pregnant.

Since ~60% of cases are asymptomatic, it's probably a sensible precaution for men with pregnant partners to use condoms during and for 2 weeks after a trip to an affected area, even if they didn't fall noticeably ill.

<self promotion> Quite a lot of people seem to like this answer I wrote on Skeptics, though the structure is a bit odd because it followed one person's specific questions and concerns. That said, that one guy's questions do seem to cover a lot of the important gaps left by the regular media.

In general, the most important things to understand are:

• For an individual, there are risks but unless you're pregnant, the risks of serious complications like Guillain-Barré are lower than the risk of serious complications for more established diseases like Dengue. Most people who get Zika have no symptoms at all. I'd much rather get Zika than Dengue or West Nile (unless I was pregnant)
• Zika's scary from a public health point of view. It spreads very, very quickly among non-Asian populations (good immunity seems common in Asia, it's the Asian strain of the disease), and since so many people's cases are asymptomatic, mild, or mistakable for things like flu, it's almost impossible to track where it's reached or where it'll appear next - until suddenly babies with small heads start getting born and small numbers of people suffer potentially serious/fatal autoimmune complications. You can't just snuff it out with a track and trace program like the ones that (almost) beat Ebola. This is why public health authorities are so concerned about it: it's hard to control, and in rare cases, is terrible. But most individuals who get it don't even realise they had it.

It's also very medically unusual - no-one understands why it causes the conditions it causes - so the authorities are being understandably extremely cautious.

Basically, don't panic, but be aware, and be careful to avoid mosquito bites (which of course you should be anyway, because of dengue fever and the non-100% effectiveness of anti-malarials).