Spain Itinerary Advice

Your timings work, I think.
However, Granada is nearer to Seville than to Valencia, so I would swap the order.
The other thought would be to cut Seville to 3 nights and stay in Cordoba for 2 nights before 2 nights in Granada.
You don't say how you are travelling, but the whole trip is possible by train.
The old Spanish cities are designed to cope with the heat, so don't worry.

There is some nonsense put out on here about Sevilla weather. Surely, it gets hot. But it is a dry heat relatively for much of the year. Even though Barcelona can appear to have a lower temperature, the humidity means that in parts of the year you'll feel much more uncomfortable - like a damp rag - than you would further South.

Anyway, June isn't unbearable in either place. And since we don't know what the actual weather will be this coming June, I wouldn't plan based on that.

I think the main issues with your plan are
i) Putting Granada and Sevilla next to each other makes more geographic sense, whether driving or using public transport, and
ii) Valencia is going to be an outlier. It isn't an easy journey from either Sevilla or Granada. It fits better between Barcelona and Madrid, and
iii) There is a huge amount to see in Barcelona. If you plan a day-trip and need to fly out from that city, then I might add a night.

Thank you!

Woops!
Yes Granada is after Seville, I wrote the order wrong.

My follow-up question would be, where would you stick Valencia then in the order?

If I leave Granada before Barcelona … wouldn’t it be easier to fly From Granada to Barcelona?

My thought process was high speed train from Valencia to Barcelona ?

You could consider Barcelona to Valencia to Madrid to Sevilla (all by rail) to Granada (rail or coach) and then back to Barcelona (fly). If you are able to arrive and depart in Barcelona, that would work, and none of the domestic journeys are very long.
Your consideration is that Madrid is a central point for the high speed railways you'd use. So if you want to arrive in Madrid and depart from Barcelona, then at some point you'll need to zigzag back. For example, you could arrive in Barcelona, go to Valencia then Madrid then Sevilla then Granada and then back to Madrid - all by railway.

Reconsider Valencia and go to Cordoba instead. Not as a day trip but stay there. It’s a delightful place to walk around. As are Sevilla and Granada. Add a night to Madrid to allow for day trips to Toledo and also one to Segovia. BCN day trips to Montserrat and to Girona.

If I only want to do Toledo as day trip , is 4 nights good for Madrid?

And if my main interest in Barcelona is gothic quarter/Elborn, Park Guell and famila Sagrad, cassa batlo plus day trip …is 4 nights also enough for Barca?

It’s so hard to decided these small but important things!

Update:
I’m dropping Valencia….

It IS hard! And just because I like somewhere doesn’t mean you or anyone else will. :)

However you now have 3 nights to add somewhere else. I am neither a huge art fan nor a big city fan. So I would be staying overnight in Toledo one night (I know you said you only wanted to do a day trip).

Plus I absolutely love Granada - there is a lot more there than the Alhambra. So I would add one of your extra nights to Granada.

I think you are right to be making some of your choices based on logistics.

I can speak to Barcelona and it's surrounding areas. I would certainly suggest a day trip up Costa Brava, I find it's criminally uhnderrated. Both Girona and Tossa de Mar are a good shout. Girona you can do a half day, maybe a morning session then head over to Tossa de Mar. Tossa is also a beautiful mediveal town worth exploringm, then head to the beach.

What I might do if I was in your shoes, and maybe you're already thinking this, is rent a car for the day, they are relatively inexpensive (25-50eur/ day depending where pickup/drop off is) You're going to save on travel time and will be able to do both Girona and Tossa de Mar if wanted to. Tossa has a great cala/beach, but there are many smaller, secluded Calas (bay, or cove) that dot the coastline just north of Tossa de Mar. Some of these calas are unreal in it's beauty, an absoule highlight of Costa Brava. I've written about the best beaches in Costa Brava , (https://www.moto-espana.com/motorcycle-travel-guide/best-beaches-near-barcelona) for motorcycle riders, but it's relevant for you as well.

Cala Futadora (about 10 minutes from Tossa, this one is super secluded, parking may be difficult if you get here later. Platja de les Barques is further up, but ample parking, this might be your best bet.

One of my favorite coastal towns is Calella de Palafrugell (about same distance from Girona as Tossa is), super quaint and has the cutest little beach with colored wooden row boats, I'd show you a picture, but can't seem to add it here. But, this town is much smaller than Tossa de Mar.

I can go on, but let me no ramble. If you want to know more, more than happy to share.

Unless there’s the possibility of a blizzard, I seldom take weather into consideration for trips. As Nick stated, nobody knows what it will be like a few months from now. Just know that much of Spain is warm to hot in June. In locations in the mountains there could still be near freezing temperatures into June.

On my Spain trips I’ve driven through areas that were hit with floods just a couple days after we passed by and drove into areas that had just reopened after major fires. A couple days earlier or later and my entire itinerary would have had to have been changed. I needed gloves because it was so cold in O’Ceibro in late May and needed to stick my feet into a fountain in Trujillo because it was so hot. Weather in unpredictable.