Advice on Tel Aviv

1. This hostel is one block from the beach and is generally recommended: http://www.hayarkon48.com/
2. It should be warm enough to sunbath at midday, but the weather is variable at that time of year and there is still a slight chance of rain and cooler weather.
3. You can take a bus from either the central bus station or the Arlozorov terminal in north Tel-Aviv. They leave every 15-20 minutes. Driving time is about an hour.

I recommend that you spend at least two days in Jerusalem - one in the Old City and one in the New City. Check out Sandeman's free walking tour: http://www.newjerusalemtours.com/daily-tours/new-jerusalem-free-tour.html

Note that the Passover holiday is April 7 to 13 this year. I recommend that you visit either before or after the holiday because during this week the sites are packed with tourists and Israelis on vacation and it is difficult to find reasonable accommodations without booking far in advance.

1/ Old Jaffa hostel is really nice, with a cool vibe and close to the beach.

2/ April is not a good time to sunbathe, no. The weather should be nice though and the beach is nice whatever the season.

3/ You can reach Jerusalem easily with the sheruts (minibuses) which depart from Tel Aviv central bus station. They're cheap and very practical.

4 / Israel is a very expensive country, often more expensive than Western Europe, so don't expect to survive on a very tight budget. Maybe you could try Couchsurfing to cut costs?

Further to what has already been written:

Read FAQ 51 to see how the Passover holiday will affect your trip if you are in Israel then.

April is unlikely to be warm enough for sunbathing. There's nothing to stop you going on the beach and you are unlikely to be alone. However, note that the bathing season starts officially on Independence Day, which this year is April 26. Before then, there are no lifeguards and it is forbidden to swim where there are no lifeguards (even if there's a heatwave). The Mediterranean is a lot more dangerous than it looks, and every year there are drowning tragedies involving tourists.

Just to correct what Shuffaluff wrote:
The bathing season starts this year on April 22. Until then there are five beaches in Tel-Aviv that have lifeguard services throughout the winter every day from 7:45 to 13:45 (but not on rainy days). The beaches are : Zuk, Nordau, Frischman, Jerusalem and Aviv.

(Shuffaluff: see http://www.tel-aviv.gov.il/ToEnjoy/Beaches/Pages/Beaches.aspx?tm=16&sm=21 )

I stand corrected on the beaches! I admit that swimming on Tel Aviv beaches is not my field of expertise.

But in any case, don't swim where there are no lifeguards.

Try Momos hostel on ben yehuda st. Sunbathing almost yearound. Plenty of transportation to Jerusalem.

I live in Jaffa, and i think Old jaffa hostel has a nice vibe, and its pretty close to the beach.

1. there is a very clean budjet hotel names Sea Net
2. its a great tome to go to the beach, not to hot and great sunbathe
3. go to gerusalem for the first day, caz it's between TLV and Jerusalem.