For that area I'd recommend a perforated hose system or drip tape - it's a universal solution that's both simple to install and pretty affordable price-wise. You can buy a ready-made kit (they go for 1,500 to 3,000 rubles) or put it together yourself: grab a regular garden hose, poke holes in it every 15-20 cm or just buy a perforated hose already. Lay it along the rows with tomatoes and cucumbers, secure it with stakes, connect it to the water supply or a well. Meanwhile you can water the greens with a regular watering can if it's a small area, or use the same hose with low pressure.
If you want to minimize fussing around, check out automatic timers for the tap - they're not expensive (500-1,500 rubles), install between the tap and hose, and they'll open and close the water on schedule by themselves. Program them, say, to water every day at 6 AM for an hour, and the soil stays moist. In my 14 years working in real estate I've seen plenty of clients use exactly this setup at their dachas - simple, reliable and cheap.
The main thing is before you leave you fill the timer with batteries, check that the hose doesn't have holes, and you can head off to the city worry-free. Your tomatoes and cucumbers will be way more grateful for regular watering than they would be from occasional but heavy hand watering.