Is it possible to obtain a 60-day tourist visa for Thailand at the embassy in Vientiane, Laos for Israeli nationals?

Remember you need to BOOK an online appointment at the thai consulate in Vientiane to get IN the gate to apply for a visa

you need to show 20K baht or the equivalent in a bank account for 3 months before you apply for the visa

AND

you need to realize they take 3 working days to issue a visa (ex; apply Monday morning, pick up your passport Wednesday afternoon).

You could go to the thai consulate in Savannakhet Lao (across the river from Mukdahan Thailand). They allow walk up application, you only show the 20K baht or equivalent in a bank account on the day you apply, and they have a 2 working day processing (ex; apply Monday morning, get your passport back Tuesday afternoon)