Hiya! I've spent quite a bit time in Israel myself as my boyfriend lives there, so I'll do my best to answer some of your questions:
For Tel Aviv Vs Haifa --
Tel Aviv is apparently the 'party central' but tbh I never had much interest in checking the veracity of this myself. It has *really* lovely cafes (my favourite are on Rothschild Boulevard), a laid back atmosphere and a great choice of beautiful beaches (although they're often packed on shabbat). It can be very humid during the summer months, though, and parking is a nightmare.
Haifa is a little more off the beaten track, with a larger Arab population and less choice in shopping and whatnot. However, it has a much more bearable climate with a nice breeze throughout the year and is a quite similar to Ireland with its greenery. In terms of accommodation, it is much cheaper than Tel Aviv.
Neither area is particularly unsafe- I would think that the most 'dangerous' place in Israel is Jerusalem, mainly due to the tension between various communities and high amount of religious wackos.
It's really a toss up between the two- I think the nature and walks of Haifa are beautiful, and you'll have a greater chance to explore the Israeli countryside up there. However, if you enjoy a vibrant atmosphere and want to live in a more 'European' area, then it's Tel Aviv.
Personally, I lived just outside Tel Aviv and found it wonderful. Close enough to enjoy the great atmosphere and go for nice lunches on shabbat but also far enough away that it wasn't so hectic. I worked up north for a while and since I didn't have much interest in hiking and nature, I just found it a little too isolated.
Cultural differences --
When trying to portray the Israeli mentality, it's impossible to do so in such a short amount of space without making major generalisations. But really, you'll understand what I mean when you get there. They can be very full on- loud, opinionated, talkative while sometimes arrogant and rather tactless. Best to avoid all talk of politics and religion, unless you want a blazing row, and always try to steer conversation away from controversial subjects if that's where they're heading. That said, you could have a big argument and right afterwards they're your best buddy again as if nothing happened. They're very loyal friends and will very often go out of their way to accommodate you. They're second to none when it comes to helpfulness.
I can't think of specific cultural differences atm. Most of it I guess is based around religion. There are different 'levels' of religiosity-- the most religious being the black suit-wearing, bearded haredim (also derogatively called 'dosim'). Don't try to shake their hand or sit beside them on the bus if you're a woman. The female dosim are pretty obvious too- long sleeves and skirts in sombre colours which appear very outdated, often with a wig or sometimes a headcovering if they are married. Same rules apply as with the males in regard to touching the opposite gender. There are then the moderately religious-- the men wear crotched kippot (head coverings, sing. 'kippa') and western style clothing. The women have long sleeves and skirts, but are more 'modern' and often have a headscarf if they are married. Religious people won't spend money or use electricity on shabbat, and nearly all shops and amenities are closed on this day. On shabbat I used to head to the nearby park with my boyfriend or else chill out at home, have a nap, watch tv, make a nice meal, or go to the beach. Buses and trains don't operate on shabbat, but sherutim (שרותים -- like yellow mini vans http://www.otzarstock.com/store/watermark.php?i=3953
) do - once you get a hang of where everything is and what routes to take, they're invaluable during the weekend or simply when you can't be bothered waiting for a bus. Taxis are also available, but hike up the cost on shabbat. The majority of Israelis (especially in Tel Aviv and Haifa) are secular and dress and behave much the same as here. On the whole, 'mizrachim' (Israelis from Arabic countries, darker in complexion) tend to be more hot-and-cold, outgoing and friendly as opposed to 'ashkenazim' (those of Eastern European descent) who can be more reserved.
How does it differ to Ireland/US life. Are there things I wont be able to get there that Id be used to--
Some things are more expensive in Israel, such as deodorant, sunscreen and various other toiletries. I recommend getting the 'own brand' stuff- you'll save a load, as the imported products with labels you're probably more familiar with are very expensive. In pharmacies, this will usually be the 'life' label.
You'll find all the major shops there (Zara, Mango, H&M) but tbh I think they're overpriced. 'Israeli' clothing shops are, in my opinion, full of cheap, ugly and ill-fitting women's clothes, but there are some serious bargains for men! Actually, if your husband wants some lovely and inexpensive polo shirts, head to HaCarmel Market in Tel Aviv- they're gorgeous, I go back every year to get presents for my dad and brother. But as a woman, I would advise you to buy your clothes in the US/Ireland and bring them with you. However, be sure to bring clothes which are comfortable, casual and breathable. People don't get dressed up for anything in Israel, so unless your husband has a seriously official job, he can leave the office wear at home. Bring your own medicines and whatnot, and make sure you have some kind of adaptor for any electrical items.
Oh-- and bring teabags if you are so inclined!! I nearly died last summer without my Barrys Tea! Buy the milk in a bag- it's cheaper. Also, shopping bags are free, but usually reused as bin bags. Watermelon and citrus fruits are gorgeous, but be sure to do your shopping in a big supermarket, and the smaller ones are a rip off. Israeli chocolate isn't great- stock up in duty free! Also, many non-kosher foods (such as haribo) are either hard to come by or not sold at all. If you bring food into work to share, make sure it's kosher so that nobody is left out. Try to avoid leaving your shopping til Thursday evening/ Friday morning, as it is absolutely packed right before shabbat.
That's all I can think of for now, but you're more than welcome to PM me if you have any questions- best of luck, you'll love it there