There is sherut service to Haifa, Jerusalem and other distant places 24/7. I don't think there's been sherut service to Tel Aviv since the trains started running.
In September the weather is always good for the beach. Undertows can be dangerous, so look for the flags on the life guard towers - red is caution (don't go out too far), black is no swimming permitted (you can wade in the water). Leave all your valuables at the hotel. Some hotels will give you a towel for the beach, or just tuck one from your room into your beach bag. Bring a little cash. Take a hat and sunscreen too. You can rent a lounge chair. I haven't been in years, but it used to be that you just sat on a vacant one (you can move it to where you want to be) and a guy would come around and collect payment. When you want to go in the water, just ask the people next to you (the beach will be crowded) to watch your stuff. Leave something on the chair so it doesn't look occupied! There are fresh water showers on the beach, so you can cool down or rinse off the salt water. I'd go to the beach first thing, before it gets too hot (and crowded) and if you really enjoy the beach, go back in the late afternoon.
The Museum is open from 10 to 6. It's about a 1/2 hour walk from your hotel.
