Can you drive around a motorcycle in 1st gear the city?

I've read that some sports bikes can do like 80mph before redlining in first gear. Could i ride a sports bike around the city an never get out of 1st or 2nd gear an ride safetly? I have a automatic 79 honda motorcycle which i like no clutch an have had a hard time riding manual bikes mostly down shifting an locking the rear wheel up. I was thinking of geting a 250 ninja or cbr to learn to shift i live in a city an don't usually go past 35mph

Sure if you want to look like a noob.

No. You like motorcycles so you should really learn to shift gears. When you downshift you just goose the gas a tiny bit for a fraction of a second as you let the clutch out and you will learn to match the engine rpm's with the lower gear ratio so the back wheel does not chirp.

I know how you're feeling.
My first motorcycle was a Honda Cub 50 with an automated clutch whereas my next bike, a Honda CG125 had a proper 4-speed gearbox with clutch.
The transition was quite difficult but I got the hang of it after a few days. It's not really all that difficult, in all honesty.
1. Engage the clutch.
2. Put it in first gear. The bike will jerk forward, which is normal.
3. Release the clutch around half way or 1/3rd (It's different from bike to bike) and slowly rev the engine. The bike will start to move forward. Disengage the clutch after a while and ride as you normally would.
4. When it's time to reach the higher gear; simple engage the clutch, get into second gear, release. Rinse and repeat.

As for downshifting:
Let the RPMs drop a bit, the wheel is going to lock up if you downshift at high RPMs. When RPMs are low enough; engage the clutch, drop a gear then release the clutch and everything should go down smoothly. Very simple.

There's also a trick called 'throttle blip' which dramatically smoothes out downshifting but don't worry too much about it for now. Just focus on riding.

I didn't learn throttle blipping until I got my first 'real' bike; a '92 Suzuki GS500.

Check out the new E-bikes. Relatively queit for less distraction and have an easy city mileage range. Shifting is rather easy also.

Oh for crying out loud, you're afraid to shift a motorcycle?

It really isn't hard. Get a mate who CAN ride to take you to an empty car park or dead quiet back street. He can show you how. Even better if there's a rider training school in your area sign up & they will show you how.
Starting off. Pull clutch lever fully in. Engage first gear. Open throttle slightly to about 2000 rpm. Ease the clutch lever out til engine revs just start to fall. Open throttle slightly more as you let the clutch out more. Try to keep engine revs fairly constant until clutch is fully released. Ie balance engine speed against clutch lever movement.
Once moving fast enough to want to change gear simply apply light upward pressure on the gear pedal then in one quick movement back off on the throttle & pull the clutch lever in, the gear pedal will click up into the next gear & you can release the clutch & roll on the throttle. With a bit of practice it takes about half a second or less.
Down changing. Apply light downward pressure on the pedal, roll off the throttle & pull in the clutch lever in one motion, the gear pedal will click down into the next gear. Before releasing the clutch open the throttle a little to raise engine revs to about what you think will be the right speed in the new gear & release the clutch lever. Again it takes less than 1/2 second. Listen to the engine's speed - it's quicker easier (& safer) than staring at the tacho.

Get a scooter and don't waste your money, they have a continuously variable transmission so they are always in the "correct" gear and you never need to touch a gear lever.

No. First, the sport bikes that can do those speeds in 1st gear are the larger ones, not a 250 ninja. Second, they scream at very high rpm's to do so, and would still be spinning pretty fast at city speeds.
Your 250 Ninja can do about 40m in 1st gear, at 14,000 rpm, about 59mph in second. It means you'd need about 10,500 on the tach for 30mph in 1st, and and 7000rpm in second. It will suck down gas like a car, run hotter, and wear out prematurely. Shifting is not a big deal, if it is, get an automatic scooter.

If you are locking the rear wheel up on downshifts, you are downshifting too quickly.

Start by letting the bike slow until you feel the engine bogging down, and take note of the RPM's. The next time watch the RPM's and downshift before you hit that number. You'll quickly learn how to hear/feel when the engine is ready to downshift.

The main problem (besides wear and tear) of riding around in first gear is that when you let off the gas, it will want to slow really quickly (unless you pull in the clutch - at which point, you might as well be shifting).

There's the option of getting a scooter - or better yet, an electric motorcycle (which don't require shifting), but I would start by learning to properly shift a motorcycle.